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Exponential Key Features - Printable Math Worksheets class 9 - Wayground

Exponential Key Features

Lizbeth Galindo

Created by Lizbeth Galindo

11 questions

9th Grade

Math

Updated Oct 2026

This Grade 9 mathematics worksheet develops students’ ability to identify and interpret key features of exponential functions. Students classify functions as showing exponential growth or decay, determine y-intercepts and horizontal asymptotes, evaluate statements about graph behavior, and select graphs that represent given functions. The 11-item practice set combines multiple-select, multiple-choice, and fill-in-the-blank questions. Students must distinguish among x-intercepts, y-intercepts, asymptotes, and increasing or decreasing behavior while reading equations and graphs. The fill-in responses also reinforce precise mathematical notation, including entering equations without spaces when instructed. This free printable worksheet includes a complete answer key and is designed for Grade 9 math instruction, independent practice, review, or a focused check of students’ understanding of exponential key features.

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Exponential Key Features

Total questions: 11

Name
Class
Date
1.

Which of the following functions have an exponential decay?

Select all that apply

a)
Which of the following functions have an exponential decay? Select all that apply

b)
Which of the following functions have an exponential decay? Select all that apply

c)
Which of the following functions have an exponential decay? Select all that apply

d)
Which of the following functions have an exponential decay? Select all that apply

e)
Which of the following functions have an exponential decay? Select all that apply

2.

Which of the following functions have an exponential growth?

Select all that apply

a)
Which of the following functions have an exponential growth? Select all that apply

b)
Which of the following functions have an exponential growth? Select all that apply

c)
Which of the following functions have an exponential growth? Select all that apply

d)
Which of the following functions have an exponential growth? Select all that apply

e)
Which of the following functions have an exponential growth? Select all that apply

3.

Which statement about the graph of y=2(4)xy=2\left(4\right)^x is NOT true?

a)

The y-intercept is (0, 2)\left(0,\ 2\right) .

b)

The graph is increasing for all values of x.

c)

The x-intercept is (−4,0)\left(-4,0\right) .

d)

The graph has a horizontal asymptote at y=0y=0 .

4.

What is the equation of the asymptote of the graph of the function y=16(0.75)xy=16\left(0.75\right)^x ?

(DO NOT USE SPACES WHEN TYPING THE EQUATION)

(a)  

5.

What is the value of the y-intercept of the graph of h(x)=12.3(4.9)xh\left(x\right)=12.3\left(4.9\right)^x ?

(DO NOT USE SPACES WHEN TYPING THE ANSWER)

(a)  

6.

What is the value of the y-intercept of the graph of g(x)=73(45)xg\left(x\right)=73\left(\frac{4}{5}\right)^x ?

(DO NOT USE SPACES WHEN TYPING THE ANSWER)

(a)  

7.

What is the value of the y-intercept of the graph of h(x)=29(5.2)xh\left(x\right)=29\left(5.2\right)^x ?

(DO NOT USE SPACES WHEN TYPING THE ANSWER)

(a)  

8.

Which graph best represents y=5(13)xy=5\left(\frac{1}{3}\right)^x ?

a)
Which graph best represents ?

b)
Which graph best represents ?

c)
Which graph best represents ?

d)
Which graph best represents ?

9.

Which statement about the graph of y=8(0.25)xy=8\left(0.25\right)^x is true?

a)

The coordinates of the x-intercept are (0.25,0)\left(0.25,0\right)

b)

The coordinates of the y-intercept are (0,8)\left(0,8\right)

c)

The equation of the asymptote is x=0x=0

d)

The graph includes the point (2,1)\left(2,1\right)

10.

Which graph best represents f(x)=2(5)xf\left(x\right)=2\left(5\right)^x ?

a)
Which graph best represents ?

b)
Which graph best represents ?

c)
Which graph best represents ?

d)
Which graph best represents ?

11.

Which statement about the graph of y=13(23)xy=\frac{1}{3}\left(\frac{2}{3}\right)^x is true?

a)

The graph has a vertical asymptote.

b)

The graph crosses the y-axis at (0,29)\left(0,\frac{2}{9}\right) .

c)

The graph has an asymptote at y=13y=\frac{1}{3} .

d)

The graph decreases from left to right.

WaygroundAnswer Key

Exponential Key Features

Total questions: 11

1.
a)

, c)

, d)

2.
b)

, e)

3.
c)

The x-intercept is (−4,0)\left(-4,0\right) .

4.
y=0
5.
12.3
6.
73
7.
29
8.
d)

9.
b)

The coordinates of the y-intercept are (0,8)\left(0,8\right)

10.
a)

11.
d)

The graph decreases from left to right.

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FAQs

What does the Exponential Key Features worksheet cover?

This Grade 9 worksheet focuses on identifying exponential growth and decay and interpreting key graph features, including y-intercepts, x-intercepts, horizontal asymptotes, and increasing or decreasing behavior. Its 11 questions use multiple-select, multiple-choice, and fill-in-the-blank formats, requiring students to classify functions, read graph information, choose representative graphs, and enter asymptote equations or intercept values.

How can I use this worksheet to teach exponential growth and decay features?

Begin with a short review of how growth and decay appear in an exponential equation and graph, then model a feature checklist: identify the type of function, locate the y-intercept, determine the asymptote, and examine the graph’s direction. Have students explain why they selected each growth or decay option before moving to the graph-selection and fill-in items. Use the true-or-false-style statement questions to prompt discussion about which graph features are supported by the equation.

What mistakes should I watch for on the Exponential Key Features worksheet?

Watch for students selecting only one answer on the multiple-select growth and decay questions, or confusing a y-intercept with an x-intercept or horizontal asymptote. Students may also choose a graph based on its general shape without checking its intercept or whether it increases or decreases. For the fill-in items, check that students enter the requested numerical value or equation exactly as directed, including omitting spaces when required.

How do I assign and grade this exponential functions worksheet?

On Wayground, assign the Exponential Key Features worksheet as either a printable PDF or a digital quiz. The worksheet includes a complete answer key for checking the multiple-select, multiple-choice, and fill-in-the-blank responses. Printable submissions can also be graded by scanning student work with the Wayground for Teachers app.

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

Use the worksheet’s Advanced Settings to adjust font spacing and font size so the graph-feature statements, answer choices, and fill-in prompts are easier to navigate. You can also enable a dyslexia-friendly font or translate the worksheet into another language when appropriate. These options apply to the worksheet file while preserving its focus on exponential growth, decay, intercepts, and asymptotes.

Where can I find more free 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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