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Algebra 2 CUA 2 - Printable Mathematics Worksheets - Wayground

Algebra 2 CUA 2

14 questions

11th - 11th Grade

Mathematics

Algebra 2 CUA 2 is a free printable Grade 11 mathematics worksheet that checks students’ understanding of function transformations, parent functions, inverses, and composition. Across 14 multiple-choice items, students identify a parent function, interpret horizontal and vertical shifts and stretches, determine a range, find and recognize inverse functions, explain how inverses are formed, use function notation, and evaluate f(g(x)) and g(f(x)). The worksheet is useful for reviewing key Algebra 2 skills before an assessment or identifying gaps in students’ procedural fluency. Its questions require students to connect symbolic equations with transformation language, switch x and y to form an inverse, distinguish inverse notation from other function notation, and substitute one function into another in the correct order. A complete answer key supports efficient checking and feedback. Teachers can use this free printable worksheet independently, as guided practice, or alongside its digital version on Wayground.

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Worksheets

Algebra 2 CUA 2

Total questions: 14

Name
Class
Date
1.
If the blue function is f(x)=x2, then the red function must be
a)
g(x)=x2-5
b)
g(x)=x2+5
c)
g(x)=(x-5)2
d)
g(x)=(x+5)2
2.
a)
f(x)=x2 + 2
b)
f(x) = (x-2)2 + 1
c)
f(x)= (x+2)2 - 1
d)
f(x)= (x+2)2 + 1
3.

Name the Parent Function

f(x)=x3f\left(x\right)=\sqrt[3]{x}  

a)

Cube Root

b)

Square Root

c)

Cubic

d)

Quadratic

4.

State the transformations of the function from the Parent Function

g(x)=(x−2)2+3g\left(x\right)=\left(x-2\right)^2+3  

a)

Shift Left 2

and

Shift Down 3

b)

Shift Right 2

and

Shift Up 3

c)

Shift Right 2

and

Shift Down 3

d)

Shift Left 2

and

Shift Up 3

5.

Describe the transformation of

the function from its Parent Function

g(x)=2∣x−7∣−3g\left(x\right)=2\left|x-7\right|-3  

a)

Vertical Stretch by 2, Shift Right 3 and Shift Down 7

b)

Vertical Stretch by 2, Shift Right 7 and Shift Down 3

c)

Vertical Stretch by 2, Shift Left 7 and Shift Down 3

d)

Horizontal Stretch by 2, Shift Right 7 and Shift Down 3

6.

​

Range: ​ ​ ​

a)
all real numbers
b)

y≥0y\ge0  

c)

y≤0y\le0  

d)

y<0y<0  

e)

y>0y>0  

7.

Find the inverse of

f(x) = 0.25x - 7

a)

f-1(x) = 4x + 7

b)

f-1(x) = -4x + 28

c)

f-1(x) = -4x - 7

d)

f-1(x) = 4x + 28

8.

How do you find an inverse?

a)

Switch x and y

b)

Flip the signs on all the x-values

c)

Flip the signs on all the y-values

d)

Do nothing

9.
The inverse of the function f(x) is written as ...
a)
f -1(x)
b)
f 2(x)
c)
f '(x)
d)
f +(x)
10.

Which is the inverse of the function shown?

a)
b)
c)
d)
11.

are these inverse functions?

a)

no

b)

yes

12.
f(x) is the same thing as ______.
a)
y
b)
x
c)
input
d)
an equation
13.

If f(x) = 4x + 5 and g(x) = x+2 find f(g(x))

a)

x+2

b)

4x+13

c)

4x+7

d)

x+5

14.

If f(x) = 4x + 5 and g(x) = x+2 find g(f(x))

a)

x+7

b)

5x+7

c)

4x+5

d)

4x+7

Answer Key

Algebra 2 CUA 2

Total questions: 14

1.
a) g(x)=x2-5
2.
b) f(x) = (x-2)2 + 1
3.
a)

Cube Root

4.
b)

Shift Right 2

and

Shift Up 3

5.
b)

Vertical Stretch by 2, Shift Right 7 and Shift Down 3

6.
c)

y≤0y\le0  

7.
d)

f-1(x) = 4x + 28

8.
a)

Switch x and y

9.
a) f -1(x)
10.
d)
11.
a)

no

12.
a) y
13.
b)

4x+13

14.
d)

4x+7

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FAQs

What does the Algebra 2 CUA 2 worksheet cover?

This Grade 11 worksheet uses 14 multiple-choice questions to assess function transformations, parent functions, range, inverse functions, function notation, and composition. Students interpret shifts and stretches from parent functions, find inverses algebraically, recognize inverse notation, determine whether functions are inverses, and evaluate compositions such as f(g(x)) and g(f(x)).

How can I use this worksheet to teach function transformations and inverses?

Use the transformation items to have students name the parent function first, then identify each horizontal shift, vertical shift, and stretch from the equation. Before the inverse-function questions, model switching x and y and solving for y, then connect that process to the notation f⁻¹(x). Finish with the composition items to discuss why f(g(x)) and g(f(x)) can produce different expressions.

What mistakes should I watch for on this function worksheet?

Students may reverse the direction of a horizontal shift, confuse a vertical stretch with a horizontal stretch, or read the constants in a transformed equation in the wrong order. In the inverse section, watch for students who change signs instead of switching x and y, write f²(x) instead of f⁻¹(x), or apply the two composition functions in the wrong order. They may also assume f(g(x)) and g(f(x)) are automatically equal.

How do I assign and grade the Algebra 2 CUA 2 worksheet?

The worksheet is available as a printable PDF and as a digital quiz on Wayground, and it includes a complete answer key. For printable submissions, you can scan student work with the Wayground for Teachers app to support faster grading. The PDF option can also help schools reduce screen time while students review transformations, inverses, and composition.

How can I differentiate this worksheet for my students?

Use the worksheet’s Advanced Settings to increase font size or spacing when students need more room to read the equations and multiple-choice options. You can also apply a dyslexia-friendly font or translate the function-transformation and inverse-function questions into another language. These adjustments preserve the worksheet’s original multiple-choice format while improving access to its symbolic notation.

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 help students build essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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