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Transformations Algebra 2 - Printable Mathematics Worksheets - Wayground

Transformations Algebra 2

15 questions

9th - 12th Grade

Mathematics

Transformations Algebra 2 is a free printable mathematics worksheet for students in Grades 9–12 who are learning to interpret and write equations for function transformations. It contains 15 questions: 11 multiple-choice items and 4 multiple-select items focused on vertical and horizontal shifts, stretches and shrinks, reflections, and combined transformations of functions and graphs. Students identify transformations from equations, select all effects represented by a function rule, describe movement between graphs, and choose equations for transformed parabolas and absolute-value functions. These varied items help students connect algebraic changes to graphical features, including direction, scale, vertex position, and axis of reflection. The worksheet includes a complete answer key, making it useful for guided practice, independent review, or assessment in Algebra 2 and related high-school mathematics courses.

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Worksheets

Transformations Algebra 2

Total questions: 15

Name
Class
Date
1.

What does the equation g(x)=2f(x) g\left(x\right)=2f\left(x\right)\  do to the graph of f(x)?

a)

Moves the graph up 2 units

b)

Vertical stretch of scale factor 2

c)

Reflects the graph across the x-axis

d)

Moves the graph 2 units to the left

2.

What does the equation

g(x) = f(x+3) g\left(x\right)\ =\ f\left(x+3\right)\  do to the graph of f(x)?

a)

Shifts the graph left three units

b)

Shifts the graph right three units

c)

Shifts the graph up three units

d)

Shifts the graph down three units

3.

What does the equation g(x)=15f(x) g\left(x\right)=\frac{1}{5}f\left(x\right)\  do to the graph of f(x)?

a)

A vertical shrink by a factor of 1/5

b)

A vertical stretch of scale factor 5

c)

A horizontal stretch by a factor of 5

d)

A horizontal shrink by a factor of 1/5

4.

What does the equation

g(x) = f(x)−4 g\left(x\right)\ =\ f\left(x\right)-4\  do to the graph of f(x)?

a)

Shifts the graph left four units

b)

Shifts the graph right four units

c)

Shifts the graph up four units

d)

Shifts the graph down four units

5.

What does the equation

g(x) = −13f(x)g\left(x\right)\ =\ -\frac{1}{3}f\left(x\right)  do to the graph of f(x)? Select all that apply

a)

Reflection across the x-axis

b)

Reflection across the y-axis

c)

Vertical shrink

d)

Vertical stretch

e)

Translation 3 units to the left

6.

What does the equation

g(x) = f(x−4)+5g\left(x\right)\ =\ f\left(x-4\right)+5  do to the graph of f(x)? Select all that apply

a)

Vertical shift up

b)

Vertical shift down

c)

Horizontal shift left

d)

Horizontal shift right

e)

Reflection across the x-axis

7.

What does the equation

g(x) = f(−3x+2)g\left(x\right)\ =\ f\left(-3x+2\right)  do to the graph of f(x)? Select all that apply

a)

Vertical stretch

b)

Horizontal shrink

c)

Horizontal shift left

d)

Horizontal shift right

e)

Reflection across the y-axis

8.

What does the equation

g(x) = −f(−x)+4g\left(x\right)\ =\ -f\left(-x\right)+4  do to the graph of f(x)? Select all that apply

a)

Vertical stretch

b)

Vertical shift up

c)

Vertical shift down

d)

Reflection across the x-axis

e)

Reflection across the y-axis

9.

Describe the transformation from dotted to solid.

a)

left 5, up 3

b)

left 3, up 5

c)

right 5, up 3

d)

right 3, up 5

10.

Find the equation of the parabola that has...

moved 3 units to the left

moved 5 units up

a)

y=(x+3)2+5y=\left(x+3\right)^2+5

b)

y=(x+5)2+3y=\left(x+5\right)^2+3

c)

y=(x−3)2+5y=\left(x-3\right)^2+5

d)

y=(x+5)2−3y=\left(x+5\right)^2-3

11.

Find the equation of the parabola that has moved...

5 units to the right

a)

y=x2+5y=x^2+5

b)

y=x2−5y=x^2-5

c)

y=(x+5)2y=\left(x+5\right)^2

d)

y=(x−5)2y=\left(x-5\right)^2

12.
How does the following move from the parent function 
y = |x|
y =  1/2|x| + 3
a)
Opens Up, Skinnier, Shift down
b)
Opens Down, Wider, Shift up
c)
Opens Up, Wider, Shift up
d)
Opens Down, Skinnier, Shift up
13.
What is the equation of the graph below?
a)
f(x) = I x + 2 I 
b)
f(x) = I x + 2 I +2
c)
f(x) = I x - 2 I +2
d)
f(x) = I x - 2 I 
14.
If the blue is f(x)=x2, the red must be
a)
g(x)=(x+3)2
b)
g(x)=(x-3)2
c)
g(x)=x2+3
d)
g(x)=x2-2
15.
What is the equation of this graph?
a)
f(x) = (x -5)2 + 1
b)
f(x) = (x - 1)2 - 5
c)
f(x) = (x + 1)2 - 5
d)
f(x) = (x + 5)2 +1
Answer Key

Transformations Algebra 2

Total questions: 15

1.
b)

Vertical stretch of scale factor 2

2.
a)

Shifts the graph left three units

3.
a)

A vertical shrink by a factor of 1/5

4.
d)

Shifts the graph down four units

5.
a)

Reflection across the x-axis

, c)

Vertical shrink

6.
d)

Horizontal shift right

, a)

Vertical shift up

7.
e)

Reflection across the y-axis

, b)

Horizontal shrink

, c)

Horizontal shift left

8.
e)

Reflection across the y-axis

, d)

Reflection across the x-axis

, b)

Vertical shift up

9.
a)

left 5, up 3

10.
a)

y=(x+3)2+5y=\left(x+3\right)^2+5

11.
d)

y=(x−5)2y=\left(x-5\right)^2

12.
c) Opens Up, Wider, Shift up
13.
d) f(x) = I x - 2 I 
14.
b) g(x)=(x-3)2
15.
b) f(x) = (x - 1)2 - 5

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FAQs

What does the Transformations Algebra 2 worksheet cover?

This worksheet practices identifying vertical and horizontal shifts, stretches and shrinks, reflections, and combinations of transformations from function equations and graphs. Its 15 items use 11 multiple-choice and 4 multiple-select questions, then apply those ideas to writing equations for transformed parabolas and absolute-value functions.

How can I use this worksheet to teach function transformations?

Introduce one transformation family at a time—shifts, scale changes, and reflections—and have students describe what changes in the graph before completing the corresponding items. Use the multiple-select questions to prompt students to justify every selected effect, then use the graph-to-equation questions to connect movement of a vertex or parent graph to the final function rule.

What mistakes should I watch for when students complete this transformations worksheet?

Students may confuse horizontal and vertical changes, especially when a change inside the input affects the graph in the opposite direction, such as a shift left or right. They may also mistake a vertical shrink for a stretch, overlook one effect in a multiple-select item, or choose the wrong sign when writing a transformed parabola or absolute-value equation.

How do I assign and grade this Transformations Algebra 2 worksheet?

Wayground provides this worksheet as a printable PDF and as a digital quiz, with a complete answer key for all 15 questions. You can grade printable submissions by scanning student work with the Wayground for Teachers app, or review responses from the digital quiz.

How does this worksheet help students connect graphs to transformation equations?

The worksheet moves beyond naming transformations by asking students to describe movement between graphs and select equations for shifted parabolas and absolute-value functions. This sequence helps students connect features such as vertex location, opening direction, and width to the signs and coefficients in a function rule.

Where can I find more worksheets like this on Wayground?

Wayground offers a comprehensive collection of free printable worksheets and practice problems across all 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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