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INSTRUCTORS Carleen Eaton Grant Fraser Eric Smith
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Lecture Comments (2)

1 answer

Last reply by: Dr Carleen Eaton
Thu Jan 7, 2016 6:31 PM

Post by Tigist Degai on December 22, 2015

in the practice questions question number one is a function but you put its not a function

Functions

  • A function is a relation in which each element of the domain is paired with exactly one element of the range.
  • A relation is a function if and only if its graph passes the vertical line test: any vertical line passes through the graph at no more than one point.
  • If f is a function, we use function notation to describe f. For example, we could write f(x) = 3x + 2. The function f can be evaluated for specific values of x, such as 5. We write f(5) = 3(5) + 2 + 17. Thus, f(5) is an element of the range of f.
  • For the function f(x), x represents the independent variable and f(x) represents the dependent variable.

Functions

Is the relation a function?
{ (3,0), ( − 4,2), ( − 2,1), ( − 1,3), (0,4),( − 2, − 1)}
  • Domain: { 3, − 4, − 2, − 1,0, − 2}
  • Domain: { 3, − 4,, − 1,0,}
Not a function
Is the relation a function?
{ (1,4), (2, − 1), (0,3), ( − 3,1), ( − 1,2),( − 3, − 2)}
  • Domain:{ 1,2,0, − 3, − 1, − 3}
  • Domain: { 1,2,0,, − 1,}
Not a function
Is the relation a function?
{ ( − 1, − 1), (0, − 3), (3,0), ( − 3,1), (1,2),(2, − 2)}
  • Domain: { − 1,0,3, − 3,1,2}
Yes, this is a function.
Let f(x) = − 2x + 8
Find f(3)
  • f(3) = − 2(3) + 8
  • f(3) = − 6 + 8
f(3) = 2
Let f(x) = − 7x + 8
Find f(6) − 9
  • f(6) = [ − 7(6) + 8] − 9
  • f(6) = [ − 42 + 8] − 9
  • f(6) = − 33 − 9
f(6) = − 42
Let g(x) = − 5x2 + 11x − 15
Find 2g( − 2)
  • g( − 2) = − 5( − 2)2 + 11( − 2) − 15
  • g( − 2) = − 5(4) + 11( − 2) − 15
  • g( − 2) = − 20 − 22 − 15
  • g( − 2) = − 55
  • 2g( − 2) = 2( − 55)
- 110
Let g(x) = − 3x3 − 4x + 5
Find 6g(2) + 2g(1)
  • g(2) = − 3(2)3 − 4(2) + 5
  • g(2) = − 3(8) − 4(2) + 5
  • g(2) = − 24 − 8 + 5
  • g(2) = − 27
  • g(1) = − 3(1)3 − 4(1) + 5
  • g(1) = − 3(1) − 4(1) + 5
  • g(1) = − 3 − 4 + 5
  • g(1) = − 2
  • 6g(2) + 2g(1)
  • 6( − 27) + 2( − 2)
− 162 − 4 = − 166
Let g(x) = 2x2 + 5
Find g(2) + 10g(1)
  • g(2) = 2(2)2 + 5
    = 2*4 + 5
    = 8 + 5
    = 13
  • 10g(1) = 10[2(1)2 + 5]
    = 10[2*1 + 5]
    = 10(2 + 5)
    = 70
g(2) + 10g(1) = 13 + 70 = 83
Do these points represent a function?
  • Use the Vertical Line Test
Yes, because there are no two or more points in the same vertical line.
Do these points represent a function?
  • Use the Vertical Line Test
No because it fails two or more points are on the same vertical line, thus having multiple values for the range.

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

Functions

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

  • Intro 0:00
  • Definition 0:14
    • Review of Relations
    • Violation of Function
    • Example: Function
  • Vertical Line Test 3:18
    • Example
  • Function Notation 6:15
    • Using f(x)
    • Example: Value Assigned
  • Example 1: Relation a Function 8:10
  • Example 2: Relation a Function 9:39
  • Example 3: Using f(x) Notation 12:20
  • Example 4: g(x) Notation 15:01