#### 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

Step: 1
y = |x + 3|
[Write the function.]
Step: 2
 x - 5 - 4 - 3 - 2 - 1 y = |x + 3| 2 1 0 1 2
[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

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

Step: 1
y = - |2x| + 1
[Write the function.]
Step: 2
 x - 2 - 1 0 1 2 y = |-2x + 1| - 3 -1 1 -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

Step: 1
y = - 3|x| + 1
[Write the function.]
Step: 2
 x - 2 - 1 0 1 2 y = |-3x + 1| - 5 -2 1 -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

Step: 1
y = |x + 3| - 2
[Write the function.]
Step: 2
 x - 6 - 5 - 4 - 3 - 2 -1 0 y = |x + 3| - 2 1 0 -1 -2 - 1 0 1
[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

Step: 1
y = |2x - 3|
[Write the function.]
Step: 2
 x -1 0 1 2 3 4 y = |2x - 3| 5 3 1 1 3 5
[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

Step: 1
y = - |x3|
[Write the function.]
Step: 2
 x -2 -1 0 1 2 y = - |x3| -8 -1 0 -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

Step: 1
y = 2|x| - 3
[Write the function.]
Step: 2
 x -3 -2 -1 0 1 2 3 y = 2|x|-3 3 1 -1 -3 -1 1 3
[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

Step: 1
y = |x - 3| - 1
[Write the function.]
Step: 2
 x 0 1 2 3 4 5 6 y = |x-3|-1 2 1 0 -1 0 1 2
[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