Dr. Carleen Eaton
Logarithms and Logarithmic Functions
Slide Duration:Table of Contents
22m 23s
 Intro0:00
 Order of Operations0:19
 Variable0:27
 Algebraic Expression0:46
 Term0:57
 Example: Algebraic Expression1:25
 Evaluate Inside Grouping Symbols1:55
 Evaluate Powers2:30
 Multiply/Divide Left to Right2:55
 Add/Subtract Left to Right3:35
 Monomials4:40
 Examples of Monomials4:52
 Constant5:27
 Coefficient5:46
 Degree6:25
 Power7:15
 Polynomials8:02
 Examples of Polynomials8:24
 Binomials, Trinomials, Monomials8:53
 Term9:21
 Like Terms10:02
 Formulas11:00
 Example: Pythagorean Theorem11:15
 Example 1: Evaluate the Algebraic Expression11:50
 Example 2: Evaluate the Algebraic Expression14:38
 Example 3: Area of a Triangle19:11
 Example 4: Fahrenheit to Celsius20:41
20m 15s
 Intro0:00
 Real Numbers0:07
 Number Line0:15
 Rational Numbers0:46
 Irrational Numbers2:24
 Venn Diagram of Real Numbers4:03
 Irrational Numbers5:00
 Rational Numbers5:19
 Real Number System5:27
 Natural Numbers5:32
 Whole Numbers5:53
 Integers6:19
 Fractions6:46
 Properties of Real Numbers7:15
 Commutative Property7:34
 Associative Property8:07
 Identity Property9:04
 Inverse Property9:53
 Distributive Property11:03
 Example 1: What Set of Numbers?12:21
 Example 2: What Properties Are Used?13:56
 Example 3: Multiplicative Inverse16:00
 Example 4: Simplify Using Properties17:18
19m 10s
 Intro0:00
 Translations0:06
 Verbal Expressions and Algebraic Expressions0:13
 Example: Sum of Two Numbers0:19
 Example: Square of a Number1:33
 Properties of Equality3:20
 Reflexive Property3:30
 Symmetric Property3:42
 Transitive Property4:01
 Addition Property5:01
 Subtraction Property5:37
 Multiplication Property6:02
 Division Property6:30
 Solving Equations6:58
 Example: Using Properties7:18
 Solving for a Variable8:25
 Example: Solve for Z8:34
 Example 1: Write Algebraic Expression10:15
 Example 2: Write Verbal Expression11:31
 Example 3: Solve the Equation14:05
 Example 4: Simplify Using Properties17:26
17m 31s
 Intro0:00
 Absolute Value Expressions0:09
 Distance from Zero0:18
 Example: Absolute Value Expression0:24
 Absolute Value Equations1:50
 Example: Absolute Value Equation2:00
 Example: Isolate Expression3:13
 No Solution3:46
 Empty Set3:58
 Example: No Solution4:12
 Number of Solutions4:46
 Check Each Solution4:57
 Example: Two Solutions5:05
 Example: No Solution6:18
 Example: One Solution6:28
 Example 1: Evaluate for X7:16
 Example 2: Write Verbal Expression9:08
 Example 3: Solve the Equation12:18
 Example 4: Simplify Using Properties13:36
17m 14s
 Intro0:00
 Properties of Inequalities0:08
 Addition Property0:17
 Example: Using Numbers0:30
 Subtraction Property1:03
 Example: Using Numbers1:19
 Multiplication Properties1:44
 C>0 (Positive Number)1:50
 Example: Using Numbers2:05
 C<0 (Negative Number)2:40
 Example: Using Numbers3:10
 Division Properties4:11
 C>0 (Positive Number)4:15
 Example: Using Numbers4:27
 C<0 (Negative Number)5:21
 Example: Using Numbers5:32
 Describing the Solution Set6:10
 Example: Set Builder Notation6:26
 Example: Graph (Closed Circle)7:08
 Example: Graph (Open Circle)7:30
 Example 1: Solve the Inequality7:58
 Example 2: Solve the Inequality9:06
 Example 3: Solve the Inequality10:10
 Example 4: Solve the Inequality13:12
25m
 Intro0:00
 Compound Inequalities0:08
 And and Or0:13
 Example: And0:22
 Example: Or1:12
 And Inequality1:41
 Intersection1:49
 Example: Numbers2:08
 Example: Inequality2:43
 Or Inequality4:35
 Example: Union4:45
 Example: Inequality5:53
 Absolute Value Inequalities7:19
 Definition of Absolute Value7:33
 Examples: Compound Inequalities8:30
 Example: Complex Inequality12:21
 Example 1: Solve the Inequality12:54
 Example 2: Solve the Inequality17:21
 Example 3: Solve the Inequality18:54
 Example 4: Solve the Inequality22:15
32m 5s
 Intro0:00
 Coordinate Plane0:20
 XCoordinate and YCoordinate0:30
 Example: Coordinate Pairs0:37
 Quadrants1:20
 Relations2:14
 Domain and Range2:19
 Set of Ordered Pairs2:29
 As a Table2:51
 Functions4:21
 One Element in Range4:32
 Example: Mapping4:43
 Example: Table and Map6:26
 OnetoOne Functions8:01
 Example: OnetoOne8:22
 Example: Not OnetoOne9:18
 Graphs of Relations11:01
 Discrete and Continuous11:12
 Example: Discrete11:22
 Example: Continous12:30
 Vertical Line Test14:09
 Example: S Curve14:29
 Example: Function16:15
 Equations, Relations, and Functions17:03
 Independent Variable and Dependent Variable17:16
 Function Notation19:11
 Example: Function Notation19:23
 Example 1: Domain and Range20:51
 Example 2: Discrete or Continous23:03
 Example 3: Discrete or Continous25:53
 Example 4: Function Notation30:05
14m 46s
 Intro0:00
 Linear Equations and Functions0:07
 Linear Equation0:19
 Example: Linear Equation0:29
 Example: Linear Function1:07
 Standard Form2:02
 Integer Constants with No Common Factor2:08
 Example: Standard Form2:27
 Graphing with Intercepts4:05
 XIntercept and YIntercept4:12
 Example: Intercepts4:26
 Example: Graphing5:14
 Example 1: Linear Function7:53
 Example 2: Linear Function9:10
 Example 3: Standard Form10:04
 Example 4: Graph with Intercepts12:25
23m 7s
 Intro0:00
 Definition of Slope0:07
 Change in Y / Change in X0:26
 Example: Slope of Graph0:37
 Interpretation of Slope3:07
 Horizontal Line (0 Slope)3:13
 Vertical Line (Undefined Slope)4:52
 Rises to Right (Positive Slope)6:36
 Falls to Right (Negative Slope)6:53
 Parallel Lines7:18
 Example: Not Vertical7:30
 Example: Vertical7:58
 Perpendicular Lines8:31
 Example: Perpendicular8:42
 Example 1: Slope of Line10:32
 Example 2: Graph Line11:45
 Example 3: Parallel to Graph13:37
 Example 4: Perpendicular to Graph17:57
23m 5s
 Intro0:00
 Slope Intercept Form0:11
 m and b0:28
 Example: Graph Using Slope Intercept0:43
 Point Slope Form2:41
 Relation to Slope Formula3:03
 Example: Point Slope Form4:36
 Parallel and Perpendicular Lines6:28
 Review of Parallel and Perpendicular Lines6:31
 Example: Parallel7:50
 Example: Perpendicular9:58
 Example 1: Slope Intercept Form11:07
 Example 2: Slope Intercept Form13:07
 Example 3: Parallel15:49
 Example 4: Perpendicular18:42
31m 5s
 Intro0:00
 Step Functions0:07
 Example: Apple Prices0:30
 Absolute Value Function4:55
 Example: Absolute Value5:05
 Piecewise Functions9:08
 Example: Piecewise9:27
 Example 1: Absolute Value Function14:00
 Example 2: Absolute Value Function20:39
 Example 3: Piecewise Function22:26
 Example 4: Step Function25:25
21m 42s
 Intro0:00
 Graphing Linear Inequalities0:07
 Shaded Region0:19
 Using Test Points0:32
 Graph Corresponding Linear Function0:46
 Dashed or Solid Lines0:59
 Use Test Point1:21
 Example: Linear Inequality1:58
 Graphing Absolute Value Inequalities4:50
 Graph Corresponding Equations4:59
 Use Test Point5:20
 Example: Absolute Value Inequality5:38
 Example 1: Linear Inequality9:17
 Example 2: Linear Inequality11:56
 Example 3: Linear Inequality14:29
 Example 4: Absolute Value Inequality17:06
17m 13s
 Intro0:00
 Systems of Equations0:09
 Example: Two Equations0:24
 Solving by Graphing0:53
 Point of Intersection1:09
 Types of Systems2:29
 Independent (Single Solution)2:34
 Dependent (Infinite Solutions)3:05
 Inconsistent (No Solution)4:23
 Example 1: Solve by Graphing5:20
 Example 2: Solve by Graphing9:10
 Example 3: Solve by Graphing12:27
 Example 4: Solve by Graphing14:54
23m 53s
 Intro0:00
 Solving by Substitution0:08
 Example: System of Equations0:36
 Solving by Multiplication7:22
 Extra Step of Multiplying7:38
 Example: System of Equations8:00
 Inconsistent and Dependent Systems11:14
 Variables Drop Out11:48
 Inconsistent System (Never True)12:01
 Constant Equals Constant12:53
 Dependent System (Always True)13:11
 Example 1: Solve Algebraically13:58
 Example 2: Solve Algebraically15:52
 Example 3: Solve Algebraically17:54
 Example 4: Solve Algebraically21:40
27m 12s
 Intro0:00
 Solving by Graphing0:08
 Graph Each Inequality0:25
 Overlap0:35
 Corresponding Linear Equations1:03
 Test Point1:23
 Example: System of Inequalities1:51
 No Solution7:06
 Empty Set7:26
 Example: No Solution7:34
 Example 1: Solve by Graphing10:27
 Example 2: Solve by Graphing13:30
 Example 3: Solve by Graphing17:19
 Example 4: Solve by Graphing23:23
28m 53s
 Intro0:00
 Solving Systems in Three Variables0:17
 Triple of Values0:31
 Example: Three Variables0:56
 Number of Solutions5:55
 One Solution6:08
 No Solution6:24
 Infinite Solutions7:06
 Example 1: Solve 3 Variables7:59
 Example 2: Solve 3 Variables13:50
 Example 3: Solve 3 Variables19:54
 Example 4: Solve 3 Variables25:50
11m 34s
 Intro0:00
 What is a Matrix0:26
 Brackets0:46
 Designation1:21
 Element1:47
 Matrix Equations1:59
 Dimensions2:27
 Rows (m) and Columns (n)2:37
 Examples: Dimensions2:43
 Special Matrices4:22
 Row Matrix4:32
 Column Matrix5:00
 Zero Matrix6:00
 Equal Matrices6:30
 Example: Corresponding Elements6:36
 Example 1: Matrix Dimension8:12
 Example 2: Matrix Dimension9:03
 Example 3: Zero Matrix9:38
 Example 4: Row and Column Matrix10:26
21m 36s
 Intro0:00
 Matrix Addition0:18
 Same Dimensions0:25
 Example: Adding Matrices1:04
 Matrix Subtraction3:42
 Same Dimensions3:48
 Example: Subtracting Matrices4:04
 Scalar Multiplication6:08
 Scalar Constant6:24
 Example: Multiplying Matrices6:32
 Properties of Matrix Operations8:23
 Commutative Property8:41
 Associative Property9:08
 Distributive Property9:44
 Example 1: Matrix Addition10:24
 Example 2: Matrix Subtraction11:58
 Example 3: Scalar Multiplication14:23
 Example 4: Matrix Properties16:09
29m 36s
 Intro0:00
 Dimension Requirement0:17
 n = p0:24
 Resulting Product Matrix (m x q)1:21
 Example: Multiplication1:54
 Matrix Multiplication3:38
 Example: Matrix Multiplication4:07
 Properties of Matrix Multiplication10:46
 Associative Property11:00
 Associative Property (Scalar)11:28
 Distributive Property12:06
 Distributive Property (Scalar)12:30
 Example 1: Possible Matrices13:31
 Example 2: Multiplying Matrices17:08
 Example 3: Multiplying Matrices20:41
 Example 4: Matrix Properties24:41
33m 13s
 Intro0:00
 What is a Determinant0:13
 Square Matrices0:23
 Vertical Bars0:41
 Determinant of a 2x2 Matrix1:21
 Second Order Determinant1:37
 Formula1:45
 Example: 2x2 Determinant1:58
 Determinant of a 3x3 Matrix2:50
 Expansion by Minors3:08
 Third Order Determinant3:19
 Expanding Row One4:06
 Example: 3x3 Determinant6:40
 Diagonal Method for 3x3 Matrices13:24
 Example: Diagonal Method13:36
 Example 1: Determinant of 2x218:59
 Example 2: Determinant of 3x320:03
 Example 3: Determinant of 3x325:35
 Example 4: Determinant of 3x329:22
28m 25s
 Intro0:00
 System of Two Equations in Two Variables0:16
 One Variable0:50
 Determinant of Denominator1:14
 Determinants of Numerators2:23
 Example: System of Equations3:34
 System of Three Equations in Three Variables7:06
 Determinant of Denominator7:17
 Determinants of Numerators7:52
 Example 1: Two Equations8:57
 Example 2: Two Equations13:21
 Example 3: Three Equations17:11
 Example 4: Three Equations23:43
22m 25s
 Intro0:00
 Identity Matrix0:13
 Example: 2x2 Identity Matrix0:30
 Example: 4x4 Identity Matrix0:50
 Properties of Identity Matrices1:24
 Example: Multiplying Identity Matrix2:52
 Matrix Inverses5:30
 Writing Matrix Inverse6:07
 Inverse of a 2x2 Matrix6:39
 Example: 2x2 Matrix7:31
 Example 1: Inverse Matrix10:18
 Example 2: Find the Inverse Matrix13:04
 Example 3: Find the Inverse Matrix17:53
 Example 4: Find the Inverse Matrix20:44
22m 32s
 Intro0:00
 Matrix Equations0:11
 Example: System of Equations0:21
 Solving Systems of Equations4:01
 Isolate x4:16
 Example: Using Numbers5:10
 Multiplicative Inverse5:54
 Example 1: Write as Matrix Equation7:18
 Example 2: Use Matrix Equations9:12
 Example 3: Use Matrix Equations15:06
 Example 4: Use Matrix Equations19:35
31m 48s
 Intro0:00
 Quadratic Functions0:12
 A is Zero0:27
 Example: Parabola0:45
 Properties of Parabolas2:08
 Axis of Symmetry2:11
 Vertex2:32
 Example: Parabola2:48
 Minimum and Maximum Values9:02
 Positive or Negative9:28
 Upward or Downward9:58
 Example: Minimum10:31
 Example: Maximum11:16
 Example 1: Axis of Symmetry, Vertex, Graph12:41
 Example 2: Axis of Symmetry, Vertex, Graph17:25
 Example 3: Minimum or Maximum21:47
 Example 4: Minimum or Maximum27:09
27m 3s
 Intro0:00
 Quadratic Equations0:16
 Standard Form0:18
 Example: Quadratic Equation0:47
 Solving by Graphing1:41
 Roots (xIntercepts)1:48
 Example: Number of Solutions2:12
 Estimating Solutions9:23
 Example: Integer Solutions9:30
 Example: Estimating9:53
 Example 1: Solve by Graphing10:52
 Example 2: Solve by Graphing15:10
 Example 1: Solve by Graphing17:50
 Example 1: Solve by Graphing20:54
19m 53s
 Intro0:00
 Factoring Techniques0:15
 Greatest Common Factor (GCF)0:37
 Difference of Two Squares1:48
 Perfect Square Trinomials2:30
 General Trinomials3:09
 Zero Product Rule5:22
 Example: Zero Product5:53
 Example 1: Solve by Factoring7:46
 Example 1: Solve by Factoring9:48
 Example 1: Solve by Factoring12:34
 Example 1: Solve by Factoring15:28
35m 45s
 Intro0:00
 Properties of Square Roots0:10
 Product Property0:26
 Example: Product Property0:56
 Quotient Property2:17
 Example: Quotient Property2:35
 Imaginary Numbers3:12
 Imaginary i3:51
 Examples: Imaginary Number4:22
 Complex Numbers7:23
 Real Part and Imaginary Part7:33
 Examples: Complex Numbers7:57
 Equality9:37
 Example: Equal Complex Numbers9:52
 Addition and Subtraction10:12
 Examples: Adding Complex Numbers10:25
 Complex Plane13:32
 Horizontal Axis (Real)13:49
 Vertical Axis (Imaginary)13:59
 Example: Labeling14:11
 Multiplication15:57
 Example: FOIL Method16:03
 Division18:37
 Complex Conjugates18:45
 Conjugate Pairs19:10
 Example: Dividing Complex Numbers20:00
 Example 1: Simplify Complex Number24:50
 Example 2: Simplify Complex Number27:56
 Example 3: Multiply Complex Numbers29:27
 Example 3: Dividing Complex Numbers31:48
27m 11s
 Intro0:00
 Square Root Property0:12
 Example: Perfect Square0:38
 Example: Perfect Square Trinomial3:00
 Completing the Square4:39
 Constant Term4:50
 Example: Complete the Square5:04
 Solve Equations6:42
 Add to Both Sides6:59
 Example: Complete the Square7:07
 Equations Where a Not Equal to 110:58
 Divide by Coefficient11:08
 Example: Complete the Square11:24
 Complex Solutions14:05
 Real and Imaginary14:14
 Example: Complex Solution14:35
 Example 1: Square Root Property18:31
 Example 2: Complete the Square19:15
 Example 3: Complete the Square20:40
 Example 4: Complete the Square23:56
22m 48s
 Intro0:00
 Quadratic Formula0:21
 Standard Form0:29
 Example: Quadratic Formula0:57
 One Rational Root3:00
 Example: One Root3:31
 Complex Solutions6:16
 Complex Conjugate6:28
 Example: Complex Solution7:15
 Discriminant9:42
 Positive Discriminant10:03
 Perfect Square (Rational)10:51
 Not Perfect Square (2 Irrational)11:27
 Negative Discriminant12:28
 Zero Discriminant12:57
 Example 1: Quadratic Formula13:50
 Example 2: Quadratic Formula16:03
 Example 3: Quadratic Formula19:00
 Example 4: Discriminant21:33
30m 7s
 Intro0:00
 Vertex Form0:12
 H and K0:32
 Axis of Symmetry0:36
 Vertex0:42
 Example: Origin1:00
 Example: k = 22:12
 Example: h = 14:27
 Significance of Coefficient a7:13
 Example: a > 17:25
 Example: a < 18:18
 Example: a > 08:51
 Example: a < 09:05
 Writing Quadratic Equations in Vertex Form10:22
 Standard Form to Vertex Form10:35
 Example: Standard Form11:02
 Example: a Term Not 114:42
 Example 1: Vertex Form19:47
 Example 2: Vertex Form22:09
 Example 3: Vertex Form24:32
 Example 4: Vertex Form28:23
27m 5s
 Intro0:00
 Graphing Quadratic Inequalities0:11
 Test Point0:18
 Example: Quadratic Inequality0:29
 Solving Quadratic Inequalities3:57
 Example: Parameter4:24
 Example 1: Graph Inequality11:16
 Example 2: Solve Inequality14:27
 Example 3: Graph Inequality19:14
 Example 4: Solve Inequality23:48
19m 29s
 Intro0:00
 Simplifying Exponential Expressions0:09
 Monomial Simplest Form0:19
 Negative Exponents1:07
 Examples: Simple1:34
 Properties of Exponents3:06
 Negative Exponents3:13
 Mutliplying Same Base3:24
 Dividing Same Base3:45
 Raising Power to a Power4:33
 Parentheses (Multiplying)5:11
 Parentheses (Dividing)5:47
 Raising to 0th Power6:15
 Example 1: Simplify Exponents7:59
 Example 2: Simplify Exponents10:41
 Example 3: Simplify Exponents14:11
 Example 4: Simplify Exponents18:04
13m 27s
 Intro0:00
 Adding and Subtracting Polynomials0:13
 Like Terms and Like Monomials0:23
 Examples: Adding Monomials1:14
 Multiplying Polynomials3:40
 Distributive Property3:44
 Example: Monomial by Polynomial4:06
 Example 1: Simplify Polynomials5:47
 Example 2: Simplify Polynomials6:28
 Example 3: Simplify Polynomials8:38
 Example 4: Simplify Polynomials10:47
31m 11s
 Intro0:00
 Dividing by a Monomial0:13
 Example: Numbers0:26
 Example: Polynomial by a Monomial1:18
 Long Division2:28
 Remainder Term2:41
 Example: Dividing with Numbers3:04
 Example: With Polynomials5:01
 Example: Missing Terms7:58
 Synthetic Division11:44
 Restriction12:04
 Example: Divisor in Form12:20
 Divisor in Synthetic Division15:54
 Example: Coefficient to 116:07
 Example 1: Divide Polynomials17:10
 Example 2: Divide Polynomials19:08
 Example 3: Synthetic Division21:42
 Example 4: Synthetic Division25:09
22m 30s
 Intro0:00
 Polynomial in One Variable0:13
 Leading Coefficient0:27
 Example: Polynomial1:18
 Degree1:31
 Polynomial Functions2:57
 Example: Function3:13
 Function Values3:33
 Example: Numerical Values3:53
 Example: Algebraic Expressions5:11
 Zeros of Polynomial Functions5:50
 Odd Degree6:04
 Even Degree7:29
 End Behavior8:28
 Even Degrees9:09
 Example: Leading Coefficient +/9:23
 Odd Degrees12:51
 Example: Leading Coefficient +/13:00
 Example 1: Degree and Leading Coefficient15:03
 Example 2: Polynomial Function15:56
 Example 3: Polynomial Function17:34
 Example 4: End Behavior19:53
33m 29s
 Intro0:00
 Graphing Polynomial Functions0:11
 Example: Table and End Behavior0:39
 Location Principle4:43
 Zero Between Two Points5:03
 Example: Location Principle5:21
 Maximum and Minimum Points8:40
 Relative Maximum and Relative Minimum9:16
 Example: Number of Relative Max/Min11:11
 Example 1: Graph Polynomial Function11:57
 Example 2: Graph Polynomial Function16:19
 Example 3: Graph Polynomial Function23:27
 Example 4: Graph Polynomial Function28:35
21m 10s
 Intro0:00
 Factoring Polynomials0:06
 Greatest Common Factor (GCF)0:25
 Difference of Two Squares1:14
 Perfect Square Trinomials2:07
 General Trinomials2:57
 Grouping4:32
 Sum and Difference of Two Cubes6:03
 Examples: Two Cubes6:14
 Quadratic Form8:22
 Example: Quadratic Form8:44
 Example 1: Factor Polynomial12:03
 Example 2: Factor Polynomial13:54
 Example 3: Quadratic Form15:33
 Example 4: Solve Polynomial Function17:24
31m 21s
 Intro0:00
 Remainder Theorem0:07
 Checking Work0:22
 Dividend and Divisor in Theorem1:12
 Example: f(a)2:05
 Synthetic Substitution5:43
 Example: Polynomial Function6:15
 Factor Theorem9:54
 Example: Numbers10:16
 Example: Confirm Factor11:27
 Factoring Polynomials14:48
 Example: 3rd Degree Polynomial15:07
 Example 1: Remainder Theorem19:17
 Example 2: Other Factors21:57
 Example 3: Remainder Theorem25:52
 Example 4: Other Factors28:21
31m 27s
 Intro0:00
 Number of Roots0:08
 Not Nature of Roots0:18
 Example: Real and Complex Roots0:25
 Descartes' Rule of Signs2:05
 Positive Real Roots2:21
 Example: Positve2:39
 Negative Real Roots5:44
 Example: Negative6:06
 Finding the Roots9:59
 Example: Combination of Real and Complex10:07
 Conjugate Roots13:18
 Example: Conjugate Roots13:50
 Example 1: Solve Polynomial16:03
 Example 2: Solve Polynomial18:36
 Example 3: Possible Combinations23:13
 Example 4: Possible Combinations27:11
31m 16s
 Intro0:00
 Equation0:08
 List of Possibilities0:16
 Equation with Constant and Leading Coefficient1:04
 Example: Rational Zero2:46
 Leading Coefficient Equal to One7:19
 Equation with Leading Coefficient of One7:34
 Example: Coefficient Equal to 18:45
 Finding Rational Zeros12:58
 Division with Remainder Zero13:32
 Example 1: Possible Rational Zeros14:20
 Example 2: Possible Rational Zeros16:02
 Example 3: Possible Rational Zeros19:58
 Example 4: Find All Zeros22:06
34m 30s
 Intro0:00
 Arithmetic Operations0:07
 Domain0:16
 Intersection0:24
 Denominator is Zero0:49
 Example: Operations1:02
 Composition of Functions7:18
 Notation7:48
 Right to Left8:18
 Example: Composition8:48
 Composition is Not Commutative17:23
 Example: Not Commutative17:51
 Example 1: Function Operations20:55
 Example 2: Function Operations24:34
 Example 3: Compositions27:51
 Example 4: Function Operations31:09
22m 42s
 Intro0:00
 Inverse of a Relation0:14
 Example: Ordered Pairs0:56
 Inverse of a Function3:24
 Domain and Range Switched3:52
 Example: Inverse4:28
 Procedure to Construct an Inverse Function6:42
 f(x) to y6:42
 Interchange x and y6:59
 Solve for y7:06
 Write Inverse f(x) for y7:14
 Example: Inverse Function7:25
 Example: Inverse Function 28:48
 Inverses and Compositions10:44
 Example: Inverse Composition11:46
 Example 1: Inverse Relation14:49
 Example 2: Inverse of Function15:40
 Example 3: Inverse of Function17:06
 Example 4: Inverse Functions18:55
30m 4s
 Intro0:00
 Square Root Functions0:07
 Examples: Square Root Function0:16
 Example: Not Square Root Function0:46
 Radicand1:12
 Example: Restriction1:31
 Graphing Square Root Functions3:42
 Example: Graphing3:49
 Square Root Inequalities8:47
 Same Technique9:00
 Example: Square Root Inequality9:20
 Example 1: Graph Square Root Function15:19
 Example 2: Graph Square Root Function18:03
 Example 3: Graph Square Root Function22:41
 Example 4: Square Root Inequalities25:37
20m 46s
 Intro0:00
 Definition of the nth Root0:07
 Example: 5th Root0:20
 Example: 6th Root0:51
 Principal nth Root1:39
 Example: Principal Roots2:06
 Using Absolute Values5:58
 Example: Square Root6:18
 Example: 6th Root8:40
 Example: Negative10:15
 Example 1: Simplify Radicals12:23
 Example 2: Simplify Radicals13:29
 Example 3: Simplify Radicals16:07
 Example 4: Simplify Radicals18:18
41m 11s
 Intro0:00
 Properties of Radicals0:16
 Quotient Property0:29
 Example: Quotient1:00
 Example: Product Property1:47
 Simplifying Radical Expressions3:24
 Radicand No nth Powers3:47
 Radicand No Fractions6:33
 No Radicals in Denominator7:16
 Rationalizing Denominators8:27
 Example: Radicand nth Power9:05
 Conjugate Radical Expressions11:47
 Conjugates12:07
 Example: Conjugate Radical Expression13:11
 Adding and Subtracting Radicals16:12
 Same Index, Same Radicand16:20
 Example: Like Radicals16:28
 Multiplying Radicals19:04
 Distributive Property19:10
 Example: Multiplying Radicals19:20
 Example 1: Simplify Radical24:11
 Example 2: Simplify Radicals28:43
 Example 3: Simplify Radicals32:00
 Example 4: Simplify Radical36:34
30m 45s
 Intro0:00
 Definition 10:20
 Example: Using Numbers0:39
 Example: NonNegative2:46
 Example: Odd3:34
 Definition 24:32
 Restriction4:52
 Example: Relate to Definition 15:04
 Example: m Not 15:31
 Simplifying Expressions7:53
 Multiplication8:31
 Division9:29
 Multiply Exponents10:08
 Raised Power11:05
 Zero Power11:29
 Negative Power11:49
 Simplified Form13:52
 Complex Fraction14:16
 Negative Exponents14:40
 Example: More Complicated15:14
 Example 1: Write as Radical19:03
 Example 2: Write with Rational Exponents20:40
 Example 3: Complex Fraction22:09
 Example 4: Complex Fraction26:22
31m 27s
 Intro0:00
 Radical Equations0:11
 Variables in Radicands0:22
 Example: Radical Equation1:06
 Example: Complex Equation2:42
 Extraneous Roots7:21
 Squaring Technique7:35
 Double Check7:44
 Example: Extraneous8:21
 Eliminating nth Roots10:04
 Isolate and Raise Power10:14
 Example: nth Root10:27
 Radical Inequalities11:27
 Restriction: Index is Even11:53
 Example: Radical Inequality12:29
 Example 1: Solve Radical Equation15:41
 Example 2: Solve Radical Equation17:44
 Example 3: Solve Radical Inequality20:24
 Example 4: Solve Radical Equation24:34
40m 54s
 Intro0:00
 Simplifying Rational Expressions0:22
 Algebraic Fraction0:29
 Examples: Rational Expressions0:49
 Example: GCF1:33
 Example: Simplify Rational Expression2:26
 Factoring 14:04
 Example: Simplify with 14:19
 Multiplying and Dividing Rational Expressions6:59
 Multiplying and Dividing7:28
 Example: Multiplying Rational Expressions8:36
 Example: Dividing Rational Expressions11:20
 Factoring14:01
 Factoring Polynomials14:19
 Example: Factoring14:35
 Complex Fractions18:22
 Example: Numbers18:37
 Example: Algebraic Complex Fractions19:25
 Example 1: Simplify Rational Expression25:56
 Example 2: Simplify Rational Expression29:34
 Example 3: Simplify Rational Expression31:39
 Example 4: Simplify Rational Expression37:50
55m 4s
 Intro0:00
 Least Common Multiple (LCM)0:27
 Examples: LCM of Numbers0:43
 Example: LCM of Polynomials4:02
 Adding and Subtracting7:55
 Least Common Denominator (LCD)8:07
 Example: Numbers8:17
 Example: Rational Expressions11:03
 Equivalent Fractions15:22
 Simplifying Complex Fractions21:19
 Example: Previous Lessons21:36
 Example: More Complex22:53
 Example 1: Find LCM28:30
 Example 2: Add Rational Expressions31:44
 Example 3: Subtract Rational Expressions39:18
 Example 4: Simplify Rational Expression38:26
57m 13s
 Intro0:00
 Rational Functions0:18
 Restriction0:34
 Example: Rational Function0:51
 Breaks in Continuity2:52
 Example: Continuous Function3:10
 Discontinuities3:30
 Example: Excluded Values4:37
 Graphs and Discontinuities5:02
 Common Binomial Factor (Hole)5:08
 Example: Common Factor5:31
 Asymptote10:06
 Example: Vertical Asymptote11:08
 Horizontal Asymptotes20:00
 Example: Horizontal Asymptote20:25
 Example 1: Holes and Vertical Asymptotes26:12
 Example 2: Graph Rational Faction28:35
 Example 3: Graph Rational Faction39:23
 Example 4: Graph Rational Faction47:28
20m 21s
 Intro0:00
 Direct Variation0:07
 Constant of Variation0:25
 Graph of Constant Variation1:26
 Slope is Constant k1:35
 Example: Straight Lines1:41
 Joint Variation2:48
 Three Variables2:52
 Inverse Variation3:38
 Rewritten Form3:52
 Examples in Biology4:22
 Graph of Inverse Variation4:51
 Asymptotes are Axes5:12
 Example: Inverse Variation5:40
 Proportions10:11
 Direct Variation10:25
 Inverse Variation11:32
 Example 1: Type of Variation12:42
 Example 2: Direct Variation14:13
 Example 3: Joint Variation16:24
 Example 4: Graph Rational Faction18:50
55m 14s
 Intro0:00
 Rational Equations0:15
 Example: Algebraic Fraction0:26
 Least Common Denominator0:49
 Example: Simple Rational Equation1:22
 Example: Solve Rational Equation5:40
 Extraneous Solutions9:31
 Doublecheck10:00
 No Solution10:38
 Example: Extraneous10:44
 Rational Inequalities14:01
 Excluded Values14:31
 Solve Related Equation14:49
 Find Intervals14:58
 Use Test Values15:25
 Example: Rational Inequality15:51
 Example: Rational Inequality 217:07
 Example 1: Rational Equation28:50
 Example 2: Rational Equation33:51
 Example 3: Rational Equation38:19
 Example 4: Rational Inequality46:49
35m 58s
 Intro0:00
 What is an Exponential Function?0:12
 Restriction on b0:31
 Base0:46
 Example: Exponents as Bases0:56
 Variables as Exponents1:12
 Example: Exponential Function1:50
 Graphing Exponential Functions2:33
 Example: Using Table2:49
 Properties11:52
 Continuous and One to One12:00
 Domain is All Real Numbers13:14
 XAxis Asymptote13:55
 YIntercept14:02
 Reflection Across YAxis14:31
 Growth and Decay15:06
 Exponential Growth15:10
 Real Life Examples15:41
 Example: Growth15:52
 Example: Decay16:12
 Real Life Examples16:30
 Equations17:32
 Bases are Same18:05
 Examples: Variables as Exponents18:20
 Inequalities21:29
 Property21:51
 Example: Inequality22:37
 Example 1: Graph Exponential Function24:05
 Example 2: Growth or Decay27:50
 Example 3: Exponential Equation29:31
 Example 4: Exponential Inequality32:54
45m 54s
 Intro0:00
 What are Logarithms?0:08
 Restrictions0:15
 Written Form0:26
 Logarithms are Exponents0:52
 Example: Logarithms1:49
 Logarithmic Functions5:14
 Same Restrictions5:30
 Inverses5:53
 Example: Logarithmic Function6:24
 Graph of the Logarithmic Function9:20
 Example: Using Table9:35
 Properties15:09
 Continuous and One to One15:14
 Domain15:36
 Range15:56
 YAxis is Asymptote16:02
 X Intercept16:12
 Inverse Property16:57
 Compositions of Functions17:10
 Equations18:30
 Example: Logarithmic Equation19:13
 Inequalities20:36
 Properties20:47
 Example: Logarithmic Inequality21:40
 Equations with Logarithms on Both Sides24:43
 Property24:51
 Example: Both Sides25:23
 Inequalities with Logarithms on Both Sides26:52
 Property27:02
 Example: Both Sides28:05
 Example 1: Solve Log Equation31:52
 Example 2: Solve Log Equation33:53
 Example 3: Solve Log Equation36:15
 Example 4: Solve Log Inequality39:19
28m 43s
 Intro0:00
 Product Property0:08
 Example: Product0:46
 Quotient Property2:40
 Example: Quotient2:59
 Power Property3:51
 Moved Exponent4:07
 Example: Power4:37
 Equations5:15
 Example: Use Properties5:58
 Example 1: Simplify Log11:17
 Example 2: Single Log15:54
 Example 3: Solve Log Equation18:48
 Example 4: Solve Log Equation22:13
25m 23s
 Intro0:00
 What are Common Logarithms?0:10
 Real World Applications0:16
 Base Not Written0:27
 Example: Base 100:39
 Equations1:47
 Example: Same Base1:56
 Example: Different Base2:37
 Inequalities6:07
 Multiplying/Dividing Inequality6:21
 Example: Log Inequality6:54
 Change of Base12:45
 Base 1013:24
 Example: Change of Base14:05
 Example 1: Log Equation15:21
 Example 2: Common Logs17:13
 Example 3: Log Equation18:22
 Example 4: Log Inequality21:52
21m 14s
 Intro0:00
 Number e0:09
 Natural Base0:21
 Growth/Decay0:33
 Example: Exponential Function0:53
 Natural Logarithms1:11
 ln x1:19
 Inverse and Identity Function1:39
 Example: Inverse Composition1:55
 Equations and Inequalities4:39
 Extraneous Solutions5:30
 Examples: Natural Log Equations5:48
 Example 1: Natural Log Equation9:08
 Example 2: Natural Log Equation10:37
 Example 3: Natural Log Inequality16:54
 Example 4: Natural Log Inequality18:16
24m 30s
 Intro0:00
 Decay0:17
 Decreases by Fixed Percentage0:23
 Rate of Decay0:56
 Example: Finance1:34
 Scientific Model of Decay3:37
 Exponential Decay3:45
 Radioactive Decay4:13
 Example: Half Life5:33
 Growth9:06
 Increases by Fixed Percentage9:18
 Example: Finance10:09
 Scientific Model of Growth11:35
 Population Growth12:04
 Example: Growth12:20
 Example 1: Computer Price14:00
 Example 2: Stock Price15:46
 Example 3: Medicine Disintegration19:10
 Example 4: Population Growth22:33
32m 42s
 Intro0:00
 Midpoint Formula0:15
 Example: Midpoint0:30
 Distance Formula2:30
 Example: Distance2:52
 Example 1: Midpoint and Distance4:58
 Example 2: Midpoint and Distance8:07
 Example 3: Median Length18:51
 Example 4: Perimeter and Area23:36
41m 27s
 Intro0:00
 What is a Parabola?0:20
 Definition of a Parabola0:29
 Focus0:59
 Directrix1:15
 Axis of Symmetry3:08
 Vertex3:33
 Minimum or Maximum3:44
 Standard Form4:59
 Horizontal Parabolas5:08
 Vertex Form5:19
 Upward or Downward5:41
 Example: Standard Form6:06
 Graphing Parabolas8:31
 Shifting8:51
 Example: Completing the Square9:22
 Symmetry and Translation12:18
 Example: Graph Parabola12:40
 Latus Rectum17:13
 Length18:15
 Example: Latus Rectum18:35
 Horizontal Parabolas18:57
 Not Functions20:08
 Example: Horizontal Parabola21:21
 Focus and Directrix24:11
 Horizontal24:48
 Example 1: Parabola Standard Form25:12
 Example 2: Graph Parabola30:00
 Example 3: Graph Parabola33:13
 Example 4: Parabola Equation37:28
21m 3s
 Intro0:00
 What are Circles?0:08
 Example: Equidistant0:17
 Radius0:32
 Equation of a Circle0:44
 Example: Standard Form1:11
 Graphing Circles1:47
 Example: Circle1:56
 Center Not at Origin3:07
 Example: Completing the Square3:51
 Example 1: Equation of Circle6:44
 Example 2: Center and Radius11:51
 Example 3: Radius15:08
 Example 4: Equation of Circle16:57
46m 51s
 Intro0:00
 What Are Ellipses?0:11
 Foci0:23
 Properties of Ellipses1:43
 Major Axis, Minor Axis1:47
 Center1:54
 Length of Major Axis and Minor Axis3:21
 Standard Form5:33
 Example: Standard Form of Ellipse6:09
 Vertical Major Axis9:14
 Example: Vertical Major Axis9:46
 Graphing Ellipses12:51
 Complete the Square and Symmetry13:00
 Example: Graphing Ellipse13:16
 Equation with Center at (h, k)19:57
 Horizontal and Vertical20:14
 Difference20:27
 Example: Center at (h, k)20:55
 Example 1: Equation of Ellipse24:05
 Example 2: Equation of Ellipse27:57
 Example 3: Equation of Ellipse32:32
 Example 4: Graph Ellipse38:27
38m 15s
 Intro0:00
 What are Hyperbolas?0:12
 Two Branches0:18
 Foci0:38
 Properties2:00
 Transverse Axis and Conjugate Axis2:06
 Vertices2:46
 Length of Transverse Axis3:14
 Distance Between Foci3:31
 Length of Conjugate Axis3:38
 Standard Form5:45
 Vertex Location6:36
 Known Points6:52
 Vertical Transverse Axis7:26
 Vertex Location7:50
 Asymptotes8:36
 Vertex Location8:56
 Rectangle9:28
 Diagonals10:29
 Graphing Hyperbolas12:58
 Example: Hyperbola13:16
 Equation with Center at (h, k)16:32
 Example: Center at (h, k)17:21
 Example 1: Equation of Hyperbola19:20
 Example 2: Equation of Hyperbola22:48
 Example 3: Graph Hyperbola26:05
 Example 4: Equation of Hyperbola36:29
18m 43s
 Intro0:00
 Conic Sections0:16
 Double Cone Sections0:24
 Standard Form1:27
 General Form1:37
 Identify Conic Sections2:16
 B = 02:50
 X and Y3:22
 Identify Conic Sections, Cont.4:46
 Parabola5:17
 Circle5:51
 Ellipse6:31
 Hyperbola7:10
 Example 1: Identify Conic Section8:01
 Example 2: Identify Conic Section11:03
 Example 3: Identify Conic Section11:38
 Example 4: Identify Conic Section14:50
47m 4s
 Intro0:00
 Linear Quadratic Systems0:22
 Example: Linear Quadratic System0:45
 Solutions2:49
 Graphs of Possible Solutions3:10
 Quadratic Quadratic System4:10
 Example: Elimination4:21
 Solutions11:39
 Example: 0, 1, 2, 3, 4 Solutions11:50
 Systems of Quadratic Inequalities12:48
 Example: Quadratic Inequality13:09
 Example 1: Solve Quadratic System21:42
 Example 2: Solve Quadratic System29:13
 Example 3: Solve Quadratic System35:02
 Example 4: Solve Quadratic Inequality40:29
21m 16s
 Intro0:00
 Sequences0:10
 General Form of Sequence0:16
 Example: Finite/Infinite Sequences0:33
 Arithmetic Sequences0:28
 Common Difference2:41
 Example: Arithmetic Sequence2:50
 Formula for the nth Term3:51
 Example: nth Term4:32
 Equation for the nth Term6:37
 Example: Using Formula6:56
 Arithmetic Means9:47
 Example: Arithmetic Means10:16
 Example 1: nth Term12:38
 Example 2: Arithmetic Means13:49
 Example 3: Arithmetic Means16:12
 Example 4: nth Term18:26
21m 36s
 Intro0:00
 What are Arithmetic Series?0:11
 Common Difference0:28
 Example: Arithmetic Sequence0:43
 Example: Arithmetic Series1:09
 Finite/Infinite Series1:36
 Sum of Arithmetic Series2:27
 Example: Sum3:21
 Sigma Notation5:53
 Index6:14
 Example: Sigma Notation7:14
 Example 1: First Term9:00
 Example 2: Three Terms10:52
 Example 3: Sum of Series14:14
 Example 4: Sum of Series18:13
23m 3s
 Intro0:00
 Geometric Sequences0:11
 Common Difference0:38
 Common Ratio1:08
 Example: Geometric Sequence2:38
 nth Term of a Geometric Sequence4:41
 Example: nth Term4:56
 Geometric Means6:51
 Example: Geometric Mean7:09
 Example 1: 9th Term12:04
 Example 2: Geometric Means15:18
 Example 3: nth Term18:32
 Example 4: Three Terms20:59
22m 43s
 Intro0:00
 What are Geometric Series?0:11
 List of Numbers0:24
 Example: Geometric Series1:12
 Sum of Geometric Series2:16
 Example: Sum of Geometric Series2:41
 Sigma Notation4:21
 Lower Index, Upper Index4:38
 Example: Sigma Notation4:57
 Another Sum Formula6:08
 Example: n Unknown6:28
 Specific Terms7:41
 Sum Formula7:56
 Example: Specific Term8:11
 Example 1: Sum of Geometric Series10:02
 Example 2: Sum of 8 Terms14:15
 Example 3: Sum of Geometric Series18:23
 Example 4: First Term20:16
18m 32s
 Intro0:00
 What are Infinite Geometric Series0:10
 Example: Finite0:29
 Example: Infinite0:51
 Partial Sums1:09
 Formula1:37
 Sum of an Infinite Geometric Series2:39
 Convergent Series2:58
 Example: Sum of Convergent Series3:28
 Sigma Notation7:31
 Example: Sigma8:17
 Repeating Decimals8:42
 Example: Repeating Decimal8:53
 Example 1: Sum of Infinite Geometric Series12:15
 Example 2: Repeating Decimal13:24
 Example 3: Sum of Infinite Geometric Series15:14
 Example 4: Repeating Decimal16:48
14m 34s
 Intro0:00
 Fibonacci Sequence0:05
 Background of Fibonacci0:23
 Recursive Formula0:37
 Fibonacci Sequence0:52
 Example: Recursive Formula2:18
 Iteration3:49
 Example: Iteration4:30
 Example 1: Five Terms7:08
 Example 2: Three Terms9:00
 Example 3: Five Terms10:38
 Example 4: Three Iterates12:41
48m 30s
 Intro0:00
 Pascal's Triangle0:06
 Expand Binomial0:13
 Pascal's Triangle4:26
 Properties6:52
 Example: Properties of Binomials6:58
 Factorials9:11
 Product9:28
 Example: Factorial9:45
 Binomial Theorem11:08
 Example: Binomial Theorem13:48
 Finding a Specific Term18:36
 Example: Specific Term19:26
 Example 1: Expand24:39
 Example 2: Fourth Term30:26
 Example 3: Five Terms36:13
 Example 4: Three Iterates45:07
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1 answer
Last reply by: DJ Sai
Mon Sep 17, 2018 9:59 PM
Post by John Stedge on June 15 at 03:45:19 PM
at 12:42 you spelled asymptote wrong
1 answer
Last reply by: Dr Carleen Eaton
Sat Nov 7, 2015 6:06 PM
Post by Peter Ke on October 21, 2015
Hi, what is a asymptote? I search it on google and I don't really get it. Can you explain it in an easier way?
0 answers
Post by julius mogyorossy on June 22, 2013
The inverse property for logs is like, 2, times 4, divided by 4, = 2.
0 answers
Post by julius mogyorossy on June 10, 2013
Dr. Eaton, again I don't know why you say x'2x12 is y, when you set the right side of the equation to 0, what I call y, it seems you are making it = x. I think the quadratic equation should not be called y or x, but the determinator, something like that. It just confused me, when you set y to 0, then you said x'2x12 is y. I am not sure why you talk about y at all when showing ex4, it does not seem that y has anything to do with that problem, or why you show a quadratic equation graph line, it seems you should have only showed a x dimension line graph. That problem is about finding values for x that make the inequality true, nothing to do with y. I kept thinking there was something I was not seeing. Again the quadratic equation factored said that part of the solution set was x>3, not, x<3, as you said, what you would call an invalid solution, I guess, and it said x>4 is possibly part of the solution set, which is true. Yes, you talked about y, but it really seems it is just about x and x, I know you said one of the x's is a y, but really for this problem it just seems like it is about x and x, it seems that is the better way to see it so as not confuse it with a regular quadraticinequality problem. It really seems the y values for this problem are irrelevant. The equation is set to 0 not to find the roots, the y's=0, but to find the solutions that also do not violate the rule to not take the root of 0 or a #<0, isn't that the case. For on kind of problem you set it to 0 to find the roots, for another to make sure not to take the log of 0 or a #<0. It seems you unnecessarily factored x'29 and x+3 twice, the first time when you combined them into a quadratic equation, killing two birds with one stone, so to speak, then again separately, unnecessarily it seemed, is this true.
1 answer
Last reply by: Dr Carleen Eaton
Sun Mar 11, 2012 7:16 PM
Post by Jeff Mitchell on March 7, 2012
Dr Carleen,
In example IV, you where checking for exclusions and said
(x+3)(x3)>0
X+3>0
X>3
X3>0
X>3
and you indicated 3 is not a valid solution
but wouldn't it be true that if x=4;
(4+3)(43)=(1)(7)>0 which is valid?
1 answer
Last reply by: Dr Carleen Eaton
Mon Nov 7, 2011 8:49 PM
Post by Jonathan Taylor on November 6, 2011
Dr Carleen would u explain how either u subtract or add x+4>9(equalities)
x=5
1 answer
Last reply by: Dr Carleen Eaton
Fri Jun 10, 2011 1:01 AM
Post by Manuel Gonzalez on June 7, 2011
aren't roots the opposite of exponents?
0 answers
Post by Edgar Rariton on March 6, 2011
The definition of a logarithm in this video begins with "First the restrictions...". That's one way to do it, but perhaps explaining that logarithms are the "opposite" of exponentials would have been better.
0 answers
Post by Wade Sias on January 27, 2011
There needs to be more complex problems like
lnx + lnx(x3) <= ln4
I feel the examples are to easy and I am struggling with these longer problems.
1 answer
Last reply by: Suhani Pant
Sat Jul 27, 2013 12:16 PM
Post by Dr Carleen Eaton on August 20, 2010
Correction to Example III at 38:42
When checking the potential solution x = 3, I should have written the original equation as log base6(x squared 6) NOT
log base6 (x squared  3). With the correct equation, substituting x = 3 would give:
logbase6(3 squared  3)
logbase6 (93)
logbase6(3)
Therefore, x = 3 is a valid solution.
I apologize for any confusion my error may have caused.