Solved Examples and Worksheet for Graphing Absolute Value Functions

Q1Which of the following graphs represents the function y = |x + 3| ?


A. Graph 4
B. Graph 3
C. Graph 2
D. Graph 1

Solutions
Share 
Step: 1
y = |x + 3|
  [Write the function.]
Step: 2
x- 5- 4- 3- 2- 1
y = |x + 3| 21012
  [Make a table of values]
Step: 3
The graph of y = |x + 3| is as shown.
  [Plot the points from the table of values of y = |x + 3| and join them with a smooth curve.]

Step: 4
Therefore, graph 1 represents the given function.
Correct Answer is :   Graph 1
Q2Which of the following graphs represents the function y = - |2x| - 1 ?


A. Graph 1
B. Graph 4
C. Graph 3
D. Graph 2

Solutions
Share 
Step: 1
y = - |2x| - 1
  [Write the function.]
Step: 2
  [Make a table of values.]

Step: 3
The graph of y = - |2x| - 1 is as shown.
  [Plot the points from the table of values of y = - |2x| - 1 and join them with a smooth curve.]

Step: 4
Therefore, graph 2 represents the given function.
Correct Answer is :   Graph 2
Q3Which of the following graphs represents the function y = - |2x| + 1 ?

A. Graph 2
B. Graph 3
C. Graph 1
D. Graph 4

Solutions
Share 
Step: 1
y = - |2x| + 1
  [Write the function.]
Step: 2
x- 2- 1012
y = |-2x + 1| - 3-11-1- 3
  [Make a table of values.]
Step: 3
The graph of y = - |2x| + 1 is as shown.
  [Plot the points from the table of values of y = - |2x| + 1 and join them with a smooth curve.]

Step: 4
Therefore, graph 3 represents the given function.
Correct Answer is :   Graph 3
Q4Which of the following graphs represents the function y = - 3|x| + 1 ?

A. Graph 2
B. Graph 4
C. Graph 3
D. Graph 1

Solutions
Share 
Step: 1
y = - 3|x| + 1
  [Write the function.]
Step: 2
x- 2- 1012
y = |-3x + 1| - 5-21-2- 5
  [Make a tableof values.]
Step: 3
The graph of y = - 3|x| + 1 is as shown.
  [Plot the points from the table of values of y = - 3|x| + 1 and join them with a smooth curve.]

Step: 4
Therefore, graph 4 represents the given function.
Correct Answer is :   Graph 4
Q5Which of the following graphs represents the function y = |x + 3| - 2?

A. Graph 2
B. Graph 4
C. Graph 3
D. Graph 1

Solutions
Share 
Step: 1
y = |x + 3| - 2
  [Write the function.]
Step: 2
x- 6- 5- 4- 3- 2 -10
y = |x + 3| - 2 10-1-2- 101
  [Make a table of values.]
Step: 3
The graph of y = |x + 3| - 2 is as shown.
  [Plot the points from the table of values of y = |x + 3| - 2 and join them with a smooth curve.]

Step: 4
Therefore, graph 1 represents the given function.
Correct Answer is :   Graph 1
Q6Which of the following graphs represents the function y = |2x - 3| ?


A. Graph 4
B. Graph 2
C. Graph 1
D. Graph 3

Solutions
Share 
Step: 1
y = |2x - 3|
  [Write the function.]
Step: 2
x-10123 4
y = |2x - 3| 531135
  [Make a table of values.]
Step: 3
The graph of y = |2x - 3| is as shown.
  [Plot the points from the table of values of y = |2x - 3| and join them with a smooth curve.]

Step: 4
Therefore, graph 2 represents the given function.
Correct Answer is :   Graph 2
Q7Which of the following graphs represents the function y = - |x3| ?


A. Graph 4
B. Graph 1
C. Graph 3
D. Graph 2

Solutions
Share 
Step: 1
y = - |x3|
  [Write the function.]
Step: 2
x-2-1012
y = - |x3| -8-10-1-8
  [Make a table of values.]
Step: 3
The graph of y = - |x3| is as shown.
  [Plot the points from the table of values of y = - |x3| and join them with a smooth curve.]

Step: 4
Therefore, graph 3 represents the given function.
Correct Answer is :   Graph 3
Q8Which of the following graphs represents the function y = 2|x| - 3 ?

A. Graph 1
B. Graph 2
C. Graph 3
D. Graph 4

Solutions
Share 
Step: 1
y = 2|x| - 3
  [Write the function.]
Step: 2
x-3-2-101 23
y = 2|x|-3 31-1-3-113
  [Make a table of values.]
Step: 3
The graph of y = 2|x| - 3 is as shown.
  [Plot the points from the table of values of y = 2|x| - 3 and join them with a smooth curve.]

Step: 4
Therefore, graph 4 represents the given function.
Correct Answer is :   Graph 4
Q9Which of the following graphs represents the function y = |x - 3| - 1 ?


A. Graph 3
B. Graph 1
C. Graph 2
D. Graph 4

Solutions
Share 
Step: 1
y = |x - 3| - 1
  [Write the function.]
Step: 2
x01234 56
y = |x-3|-1  210-1012
  [Make a table of values.]
Step: 3
The graph of y = |x - 3| - 1 is as shown.
  [Plot the points from the table of values of y = |x - 3| - 1 and join them with a smooth curve.]

Step: 4
Therefore, graph 3 represents the given function.
Correct Answer is :   Graph 3

HighSchool Math