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Absolute Value Functions 2nd Review - Printable Mathematics Worksheets class 11 - Wayground

Absolute Value Functions 2nd Review

12 questions

10th - 11th Grade

Mathematics

Absolute Value Functions 2nd Review is a Grade 10–11 mathematics worksheet with 12 questions covering equation and inequality solving, graph interpretation, and function transformations. Four multiple-select items ask students to solve absolute value equations and inequalities, check their answers, and show their work. Six multiple-choice questions focus on domain in interval notation, function descriptions, minimum values, vertices, lines of symmetry, and graph-based transformations. Two open-ended questions ask students to identify symmetry and a minimum and describe a transformation. Designed for review, independent practice, or formative assessment, this worksheet helps students connect algebraic solutions to the features of absolute value graphs. Students practice recognizing how a graph communicates its vertex, minimum, domain, and symmetry while explaining transformations in function notation. It is a free printable worksheet with a complete answer key for Grade 10 and Grade 11 mathematics instruction.

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Worksheets

Absolute Value Functions 2nd Review

Total questions: 12

Name
Class
Date
1.

Solve the absolute value equations below. Check your answers.  Show all your work.

∣6x+6∣−3=33|6x+6|-3=33  

a)

x=5

b)

x=-7

c)

x=6

d)

x=-8

2.

Solve the absolute value equations below. Check your answers.  Show all your work.

∣−10+5x∣=15x|-10+5x|=15x  

a)

x=-2

b)

x=-1

c)

x= 12\frac{1}{2}  

d)

x=2

3.

Solve the absolute value inequality below.

3∣9−3x∣+5≤143|9-3x|+5\le14  

a)

x ≥\ge  -6

b)

x ≥\ge  2

c)

x ≤\le  -2

d)

x ≥\ge  5

e)

x ≤\le  4

4.

Solve the absolute value inequality below.

∣−5−2x∣5<5\frac{\left|-5-2x\right|}{5}<5  

a)

x<25

b)

x>-15

c)

x>15

d)

x<10

e)

x>5

5.

What is the domain for the following graph in interval notation?

a)

(−∞,∞)\left(-\infty,\infty\right)  

b)

( −∞-\infty  , 3]

c)

( −∞-\infty  , 3)

d)

[-2,4]

6.

Given the graph, describe the absolute value function. Write it down on your paper.

a)

f(x)=∣x+1∣+3f\left(x\right)=\left|x+1\right|+3  

b)

f(x)=∣x−1∣+3f\left(x\right)=\left|x-1\right|+3  

c)

f(x)=−∣x−1∣+3f\left(x\right)=-\left|x-1\right|+3  

d)

f(x)=−∣x+3∣−1f\left(x\right)=-\left|x+3\right|-1  

e)

f(x)=−∣x−3∣+1f\left(x\right)=-\left|x-3\right|+1  

7.

What is the minimum value of the function over the interval [-4, 0]?

a)

0

b)

2

c)

-2

d)

-1

e)

-3

8.

What is the vertex?

a)

(-2,4)

b)

(-1,3)

c)

(-2,0)

d)

(4,0)

e)

(1,3)

9.

What is the symmetry of the given graph?

a)

y=-2

b)

y=3

c)

y=1

d)

x=1

e)

x=3

10.

What is the symmetry and minimum for the following function?

f(x)=12∣x−2∣+3f\left(x\right)=\frac{1}{2}\left|x-2\right|+3  

4 lines
11.

Describe the transformation to the given function.

12f(x−2)−4\frac{1}{2}f\left(x-2\right)-4  

4 lines
12.

From the given graph, make the following transformations to make a new g(x) function.

12f(x−2)−4\frac{1}{2}f\left(x-2\right)-4  

a)

g(x)=12∣x−2∣−4g\left(x\right)=\frac{1}{2}\left|x-2\right|-4  

b)

g(x)=12∣x−3∣−1g\left(x\right)=\frac{1}{2}\left|x-3\right|-1  

c)

g(x)=12∣x−1∣−1g\left(x\right)=\frac{1}{2}\left|x-1\right|-1  

d)

g(x)=12∣x+1∣−1g\left(x\right)=\frac{1}{2}\left|x+1\right|-1  

e)

g(x)=12∣x+3∣+7g\left(x\right)=\frac{1}{2}\left|x+3\right|+7  

Answer Key

Absolute Value Functions 2nd Review

Total questions: 12

1.
a)

x=5

, b)

x=-7

2.
c)

x= 12\frac{1}{2}  

3.
a)

x ≥\ge  -6

, c)

x ≤\le  -2

4.
b)

x>-15

, d)

x<10

5.
a)

(−∞,∞)\left(-\infty,\infty\right)  

6.
c)

f(x)=−∣x−1∣+3f\left(x\right)=-\left|x-1\right|+3  

7.
c)

-2

8.
e)

(1,3)

9.
d)

x=1

10.
n/a
11.
n/a
12.
b)

g(x)=12∣x−3∣−1g\left(x\right)=\frac{1}{2}\left|x-3\right|-1  

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FAQs

What does the Absolute Value Functions 2nd Review worksheet cover?

This 12-question review worksheet builds skill with solving absolute value equations and inequalities, interpreting absolute value graphs, and describing transformations. Its format combines multiple-select and multiple-choice questions with two open-ended prompts, requiring students to identify features such as domain, vertex, minimum, and line of symmetry and to explain function transformations.

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

Begin by modeling how an absolute value equation can produce more than one solution and how an inequality describes a range of values. Then have students work through the multiple-select equation and inequality items, checking their reasoning before moving to the graph questions on domain, vertex, minimum, and symmetry. Use the open-ended prompts to have students explain how a graph’s features and transformations relate to its function.

What mistakes should I watch for when students complete this absolute value functions worksheet?

Watch for students giving only one solution to an absolute value equation, reversing the solution regions for an absolute value inequality, or selecting values without checking the original equation. In the graph items, students may confuse the vertex with the line of symmetry, read domain incorrectly in interval notation, or identify a minimum from the wrong coordinate. Students may also describe a transformation without accounting for whether a change is horizontal or vertical.

How do I assign and grade this Absolute Value Functions 2nd Review worksheet?

The worksheet is available as a printable PDF and as a digital quiz on Wayground, and it includes a complete answer key. You can grade printable submissions by scanning student work with the Wayground for Teachers app. The printable version also gives schools an option for reducing screen time while students practice absolute value functions.

How can I differentiate this absolute value functions worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing and font size so the equation, graph, and open-ended transformation prompts are easier to read. You can also enable a dyslexia-friendly font or translate the worksheet into another language when appropriate for your learners.

Where can I find more worksheets like this on Wayground?

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

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