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INSTRUCTORS Carleen Eaton Grant Fraser Eric Smith
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For more information, please see full course syllabus of Algebra 1
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  • Practice Questions

  • Download Lecture Slides

  • Table of Contents

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Lecture Comments (6)

0 answers

Post by musse Wacays on July 26, 2015

okay

1 answer

Last reply by: Dr Carleen Eaton
Wed Jun 26, 2013 11:33 PM

Post by Taylor Wright on June 17, 2013

In example 3:

Couldn't X and Y be greater than or equal to 0?

1 answer

Last reply by: Dr Carleen Eaton
Sun Jan 27, 2013 12:51 PM

Post by Nathanael Shim on January 24, 2013

i am still a little confused by domain and range. could you explain to me again?

0 answers

Post by Aniket Dhawan on October 11, 2012

Great teaching,
this helped me a lot.

Thanks

Functions and Graphs

  • A function is a rule in which each value assigned to the function (each input) produces exactly one output.
  • Functions are graphed on the coordinate plane.
  • The input value is called the independent variable and the output is called the dependent variable.
  • A relation is a set of ordered pairs. The set of all first terms is called the domain of the relation. The set of second terms is called the range of the relation.
  • A discrete function has a graph consisting of isolated points that are not connected.
  • A continuous function has a graph that is a smooth curve or line.

Functions and Graphs

The function f is given by the table
x
line
1
2
3
4
5
y
line
5
6
7
2
0

Plot its graph
  • Find coordinate points
    (1,5),(2,6),(3,7),(4,2),(5,0)
Chart the points
The function f is given by the table
x
line
1
2
3
4
5
y
line
1
3
5
7
9

Plot its graph
  • Find coordinate points
    (1,1),(2,3),(3,5),(4,7),(5,9)
Chart the points
The function f is given by the table
x
line
− 2
− 1
0
1
2
y
line
− 2
6
− 5
− 9
8

Plot its graph
  • Find coordinate points
    ( - 2,2),( - 1,6),(0, - 5),(1, - 9),(2,8)
Chart the points
The function f is given by the table
x
line
0
3
− 9
− 4
7
y
line
− 2
− 3
1
6
5

Plot its graph
  • Find coordinate points
    (0, - 2),(3, - 3),( - 9,1),( - 4,6),(7,5)
Chart the points
Suppose gas costs $4.00 per gallon. Make a table that shows the costs of buying gas from 1 to 5 gallons.
Create a table with gallons as independent and cost as dependent
  • gallons
    line
    1
    2
    3
    4
    5
    cost
    line
  • Calculate the costs from the independent values
gallons
line
1
2
3
4
5
cost
line
4
8
12
16
20
Consider the data found in the previous problem, and make a graph from the table
  • Find the coordinate pairs from the table
    (1,4),(2,8),(3,12),(4,16),(5,20)
  • Chart the graph with the appropriate dependent and independent axises
  • Chart the graph with the coordinate points
A shipping company charges $3.50 per pound to send a package. The company rounds up to the next pound to calculate the cost, and maximum allowed weight is 9 pounds. What is the domain and range of of the function which represents the company's costs?
  • Consider what values are dependent and independent
Domain (weight in pounds) = 0 < x ≤ 9
Range (cost in $ ) = { 3.5, 7, 10.5, ..., 31.5}
Consider the same shipping company from the previous question with the same costs. What are the first 5 ordered pairs from its data?
  • Remember what's the domain and range of the function
Weight(lb)
line
1
2
3
4
5
Cost ($ )
line
3.5
7
10.5
14
17.5
Graph the company's shipping rates
  • Utilize and expand the data from the previous problem
Another shipping company has a flat rate of $20.50 for shipping. If you were shipping a batch of cookies which weighed 5.5 pounds, should you use the original shipping company as described in the previous three questions?
  • Remember the weight properties of the original the shipping company
No, because at 5.5 pounds the costs would be $21 which is more expensive.

*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 and Graphs

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
  • Functions 0:15
    • Example: Function
    • Example: Not Functions (Relations)
  • Graphs 4:44
    • Visual Display
    • Example: X and Y
    • Coordinate Pairs
    • Discrete Function
    • Continuous Function
  • Vertical Line Test 10:55
    • Test if Function
    • Example: Pass Through Points
  • Domain and Range 14:13
    • Example
  • Example 1: Function Given by Table 16:24
  • Example 2: Cost of Gas 18:46
  • Example 3: Cost of Gas 23:15
  • Example 4: Cost of Mail 29:07