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Algebra 2 Graphing Exponential Functions

20 questions

9th Grade

Mathematics

This Grade 9 mathematics worksheet develops students’ ability to analyze and graph exponential functions. Across 20 questions—19 multiple-choice items and one graphing task—students identify exponential equations from graphs, distinguish growth from decay, determine domain and range, find horizontal asymptotes, describe transformations, and state intervals of increase or decrease. Students use visual and algebraic evidence to connect an exponential function’s equation with its graph, including vertical shifts and reflected or decreasing behavior. The free printable worksheet is useful for guided practice, independent work, or a skills check after instruction on graphing exponential functions. It includes a complete answer key for efficient review and grading.

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Algebra 2 Graphing Exponential Functions

Total questions: 20

Name
Class
Date
1.

What is the equation that best represents the graph?

a)

y=2y

b)

y=2x

c)

y=2-x

d)

y=x2

2.

Is the pictured graph growth, decay, linear or none?  

a)

Exponential Growth

b)

Exponential Decay

c)

Linear

d)

None

3.

What is the range of this function? 

a)

(-∞,0)

b)

(0,∞)

c)

(-∞,4)

d)

(4,∞)

4.

What is the equation that represents the exponential function in the image below?

a)

y=3(½)x

b)

y=3(2)x

c)

y=(2)x

d)

y=2(3)x

5.

Graph the following exponential function.

g(x)=4(12)xg\left(x\right)=4\left(\frac{1}{2}\right)^x

6.

Which equation best describes the graph? 

a)

y = 2x + 4

b)

y = 2x - 3

c)

y = 2x - 4

d)

y = 2x + 3 

7.

What is the range of this graph?

a)

(-∞, ∞)

b)

(0, -4)

c)

(-6, ∞)

d)

(-∞, -6)

8.

What is the horizontal asymptote of the following exponential function?
y=3x+3 -1

a)

y=-1

b)

y=3

c)

y=0

d)

y=26

9.

What is the horizontal asymptote of the following exponential function?
y= -(4)x+2  - 1

a)

y=-17

b)

y=-1

c)

y= -4

d)

y=-9

10.

Is the pictured graph growth, decay, or linear or none?  

a)

Growth

b)

Decay

c)

Linear

d)

None

11.

Is this exponential growth or decay?

a)

Growth

b)

Decay

12.

Is this exponential growth or decay?

a)

Growth

b)

Decay

13.

State the interval of increasing/decreasing

a)

Increasing: (∞, -∞)

b)

Increasing: (-∞,∞)

c)

Decreasing: (∞, -∞)

d)

Decreasing: (-∞,∞)

14.

What transformations occur in the following function?

a)

right 3, up 2

b)

left 3, up 2

c)

left 3, down 2

d)

right 3, down 2

15.

Find the domain.

a)

(-∞, 4)

b)

(-∞, 1)

c)

(-∞, ∞)

d)

(∞, -∞)

16.

What is the Horizontal Asymptote?

a)

4

b)

0

c)

-1

d)

5

17.

Where is the Horizontal Asymptote?

a)

2

b)

-2

c)

4

d)

0

18.

What transformation is not present in the following equation?
y=(3)x+3 -1

a)

horizontal shift to the left 3

b)

horizontal shift to the right 3

c)

vertical shift up 1

d)

All the above are present

19.

Given g(x)=5x
Write a function that is reflected over x axis and translated 4 units to the right. 

a)

f(x)= -5x-4

b)

f(x)= -5x+4

c)

f(x)= 5(x-4)

d)

f(x)= 5-(x-4)

20.

What is the range of this graph? (output values)

a)

(4, ∞)

b)

(∞, 4)

c)

(-4, 4)

d)

(-infinity, infinity)

Answer Key

Algebra 2 Graphing Exponential Functions

Total questions: 20

1.
b)

y=2x

2.
a)

Exponential Growth

3.
d)

(4,∞)

4.
b)

y=3(2)x

5.
6.
c)

y = 2x - 4

7.
c)

(-6, ∞)

8.
a)

y=-1

9.
b)

y=-1

10.
b)

Decay

11.
a)

Growth

12.
b)

Decay

13.
d)

Decreasing: (-∞,∞)

14.
a)

right 3, up 2

15.
c)

(-∞, ∞)

16.
a)

4

17.
a)

2

18.
b)

horizontal shift to the right 3

19.
a)

f(x)= -5x-4

20.
a)

(4, ∞)

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FAQs

What does this exponential functions worksheet cover?

This Grade 9 worksheet uses 19 multiple-choice questions and one graphing task to build skill with exponential functions. Students match equations to graphs, classify growth and decay, determine domain and range, identify horizontal asymptotes, describe shifts, state increasing or decreasing intervals, and graph an exponential function.

How can I use this worksheet to teach graphing exponential functions?

Introduce the worksheet by reviewing how the base, vertical shift, and horizontal shift appear in an exponential graph. Have students explain their choices for the equation-from-graph and asymptote questions, then use the final graphing task to apply those features by plotting a function. Ask students to justify whether a graph shows growth or decay using its left-to-right behavior and equation.

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

Students may confuse growth with decay, especially when interpreting a graph without checking whether it rises or falls from left to right. They may also treat the vertical shift as the horizontal asymptote incorrectly, confuse domain with range, or reverse the direction of a horizontal transformation. In the graphing item, check that students show the correct shift and overall exponential shape rather than drawing a linear graph.

How do I assign and grade this exponential functions worksheet?

The worksheet is available as a printable PDF and as a digital quiz on Wayground, and it includes a complete answer key for checking the equation, graph, domain, range, asymptote, and transformation responses. For printable submissions, you can grade student work by scanning it with the Wayground for Teachers app.

How can I differentiate this exponential functions worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing and font size so the graph-identification choices, interval notation, and graphing directions are easier to read. You can also select a dyslexia-friendly font or translate the worksheet into another language when helpful for students working with the exponential-function vocabulary and instructions.

Where can I find more 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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