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Graphing Absolute Value Functions - Printable Math Worksheets grade 12 - Wayground

Graphing Absolute Value Functions

Kelly Enochs

Created by Kelly Enochs

11 questions

9th - 12th Grade

Math

Updated Oct 2026

This Grade 9–12 Algebra II mathematics worksheet gives students 11 multiple-choice questions on matching graphs to equations of absolute value functions. Students identify horizontal and vertical translations, reflections across the x-axis, and changes in width represented by equations such as y = |3x| and y = |1/3x|. Later items combine several transformations, including a reflected, shifted, and vertically scaled absolute value function. The worksheet is designed for guided practice, independent review, homework, or a quick formative assessment after introducing transformations in absolute value functions. Students must read each graph for its vertex, opening direction, horizontal position, vertical position, and width, then select the equation that represents all observed features. This free printable worksheet includes a complete answer key, making it useful for Grade 9–12 learners who are building accuracy with graph-to-equation interpretation and checking whether multiple transformations have been applied correctly.

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Graphing Absolute Value Functions

Total questions: 11

Name
Class
Date
1.
Choose the correct equation for the graph.

Choose the correct equation for the graph.

a)

 y=∣x+2∣y=\left|x+2\right|

b)

y=∣x−2∣y=\left|x-2\right|

c)

y=∣x∣+2y=\left|x\right|+2

d)

y=∣x∣−2y=\left|x\right|-2

2.
Choose the correct equation for the graph.

Choose the correct equation for the graph.

a)

 y=∣x+2∣y=\left|x+2\right|

b)

y=∣x−2∣y=\left|x-2\right|

c)

y=∣x∣+2y=\left|x\right|+2

d)

y=∣x∣−2y=\left|x\right|-2

3.
Choose the correct equation for the graph.

Choose the correct equation for the graph.

a)

 y=∣x+2∣y=\left|x+2\right|

b)

y=∣x−2∣y=\left|x-2\right|

c)

y=∣x∣+2y=\left|x\right|+2

d)

y=∣x∣−2y=\left|x\right|-2

4.
Choose the correct equation for the graph.

Choose the correct equation for the graph.

a)

 y=∣x+2∣y=\left|x+2\right|

b)

y=∣x−2∣y=\left|x-2\right|

c)

y=∣x∣+2y=\left|x\right|+2

d)

y=∣x∣−2y=\left|x\right|-2

5.
Choose the correct equation for the graph.

Choose the correct equation for the graph.

a)

y=∣x∣y=\left|x\right|

b)

y=∣−x∣y=\left|-x\right|

c)

y=−∣x∣y=-\left|x\right|

d)

y=∣x+4∣y=\left|x+4\right|

6.
Choose the correct equation for the graph.

Choose the correct equation for the graph.

a)

y=∣x+3∣−4y=\left|x+3\right|-4

b)

y=∣x−3∣−4y=\left|x-3\right|-4

c)

y=∣x+3∣+4y=\left|x+3\right|+4

d)

y=∣x−3∣+4y=\left|x-3\right|+4

7.
Choose the correct equation for the graph.

Choose the correct equation for the graph.

a)

y=∣x−6∣−3y=\left|x-6\right|-3

b)

y=∣x−6∣+3y=\left|x-6\right|+3

c)

y=∣x+6∣+3y=\left|x+6\right|+3

d)

y=∣x+6∣−3y=\left|x+6\right|-3

8.
Choose the correct equation for the graph below.

Choose the correct equation for the graph below.

a)

y=∣x−4∣−3y=\left|x-4\right|-3

b)

y=−∣x+4∣−3y=-\left|x+4\right|-3

c)

y=−∣x−4∣−3y=-\left|x-4\right|-3

d)

y=−∣x+4∣+3y=-\left|x+4\right|+3

9.
Choose the correct equation for the graph.

Choose the correct equation for the graph.

a)

y=∣x∣+3y=\left|x\right|+3

b)

y=∣x−3∣y=\left|x-3\right|

c)

y=−∣3x∣y=-\left|3x\right|

d)

y=∣3x∣y=\left|3x\right|

10.
Choose the correct equation for the graph.

Choose the correct equation for the graph.

a)

y=∣3x∣y=\left|3x\right|

b)

y=∣13x∣y=\left|\frac{1}{3}x\right|

c)

y=−∣13x∣y=-\left|\frac{1}{3}x\right|

d)

y=∣x−13∣y=\left|x-\frac{1}{3}\right|

11.
Choose the correct equation for the graph.

Choose the correct equation for the graph.

a)

y=−∣3x+5∣+1y=-\left|3x+5\right|+1

b)

y=∣2x−5∣+1y=\left|2x-5\right|+1

c)

y=−∣2x−5∣−1y=-\left|2x-5\right|-1

d)

y=−∣3x−5∣+1y=-\left|3x-5\right|+1

WaygroundAnswer Key

Graphing Absolute Value Functions

Total questions: 11

1.
c)

y=∣x∣+2y=\left|x\right|+2

2.
d)

y=∣x∣−2y=\left|x\right|-2

3.
a)

 y=∣x+2∣y=\left|x+2\right|

4.
b)

y=∣x−2∣y=\left|x-2\right|

5.
c)

y=−∣x∣y=-\left|x\right|

6.
a)

y=∣x+3∣−4y=\left|x+3\right|-4

7.
b)

y=∣x−6∣+3y=\left|x-6\right|+3

8.
c)

y=−∣x−4∣−3y=-\left|x-4\right|-3

9.
d)

y=∣3x∣y=\left|3x\right|

10.
b)

y=∣13x∣y=\left|\frac{1}{3}x\right|

11.
d)

y=−∣3x−5∣+1y=-\left|3x-5\right|+1

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FAQs

What does this worksheet cover, and how does it help students interpret absolute value graphs?

This worksheet covers matching graphs to equations of transformed absolute value functions through 11 multiple-choice items. Students use each graph’s vertex, opening direction, horizontal and vertical shifts, and width to distinguish equations such as y = |x + 2|, y = −|x − 4| − 3, and y = |3x|. This builds the skill of interpreting several graph transformations together rather than recognizing only the parent function.

How can I use this worksheet to teach graphing transformations of absolute value functions?

Introduce the parent graph y = |x|, then have students annotate a few worksheet graphs by locating the vertex and identifying whether the graph opens upward or downward. Ask them to determine the horizontal shift before reading the vertical shift, and then compare the graph’s width with the coefficients 3 and 1/3. Use the multiple-choice options to discuss why changing a sign inside the absolute value, outside it, or on the constant produces a different graph.

What mistakes should I watch for when students match these graphs to equations?

Students may reverse the direction of a horizontal shift, choosing y = |x − 2| for a graph shifted left or y = |x + 2| for one shifted right. They may also confuse a vertical reflection with a vertical shift, overlook the negative sign in equations such as y = −|3x − 5| + 1, or treat 3x and 1/3x as horizontal shifts instead of changes in width. Have students verify every selected equation against the vertex, opening direction, and steepness shown in the graph.

How do I assign and grade this absolute value graphing worksheet?

The worksheet is available as a printable PDF and as a digital quiz on Wayground, and it includes a complete answer key for all 11 multiple-choice questions. You can assign the digital version for online responses or print copies for written work. Printable submissions can be graded by scanning student work with the Wayground for Teachers app.

How can I differentiate this worksheet for students who need a more accessible format?

In the worksheet’s Advanced Settings, adjust font spacing or choose a larger font size to make the absolute value equations and multiple-choice options easier to read alongside the graphs. You can also apply a dyslexia-friendly font or translate the worksheet into another language when appropriate. These file-level options can support clearer access to the graph-to-equation tasks without changing the mathematical content.

Where can I find more free worksheets like this on Wayground?

Wayground offers a comprehensive collection of free printable worksheets and practice problems across subjects, with downloadable PDFs and answer keys to support essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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