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Lesson 1-3: Piecewise Functions Practice - Printable Math Worksheets 10th Grade - Wayground

Lesson 1-3: Piecewise Functions Practice

Michelle Wise

Created by Michelle Wise

15 questions

10th Grade

Math

Updated Sep 2026

This Grade 10 mathematics worksheet gives students focused practice with piecewise and step functions through 15 multiple-choice questions. Students evaluate function values such as f(0), f(4), f(-2), and g(7), identify domain restrictions for individual pieces, interpret pictured graphs, recognize step-function characteristics, and select functions that represent graphs. The set also connects step functions to practical situations, including rental pricing and postage rates. The worksheet is designed to help students move between function notation, graph features, interval restrictions, and real-world piecewise pricing rules. It is useful for independent practice, guided review, homework, or a quick check of understanding after instruction on Lesson 1-3 concepts. This free printable worksheet includes a complete answer key, helping teachers review students’ choices and identify whether errors come from substitution, endpoint interpretation, graph reading, or recognizing the structure of a step function.

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Lesson 1-3: Piecewise Functions Practice

Total questions: 15

Name
Class
Date
1.
What is f when x equals 0 ?
What is f when x equals 0?
a)
-5
b)
0
c)
1/2
d)
1
2.
Graph

Graph

a)
Graph
b)
Graph
c)
Graph
d)
Graph
3.
What is the domain restriction of the blue piece of this function?
What is the domain restriction of the blue piece of this function?
a)
x > 0
b)
x ≥ 0
c)
x > 2
d)
x ≥ 2
4.
What is f when x equals 4 ?
What is f when x equals 4?
a)
-5
b)
0
c)
3
d)
6
5.
What is g(7) if:
What is g(7) if:
a)
-17
b)
-13 
c)
13       
d)
17
6.
What is f(-2)?
What is f(-2)?
a)
4
b)
1
c)
1
d)
DNE
7.
What is the domain restriction for the green piece of this function?

What is the domain restriction for the green piece of this function?

a)

-2 < x ≤ 1

b)

-1 < x ≤ 0.5

c)

x > -2

d)

x ≤ 1

8.
Evaluate f(0)

Evaluate f(0)

a)

0

b)

19

c)

9

d)

-19

9.
Using the pictured graph, what is f(-3)?
Using the pictured graph, what is f(-3)? 
a)
-3
b)
-1
c)
1
d)
3
10.
What is the value of f(0)?
What is the value of f(0)?
a)
-2
b)
2
c)
4
d)
0
11.
1. What is this type of function called?

1. What is this type of function called?

a)

Continuous Function

b)

Absolute Value Function

c)

Step Function

d)

Jump Function

e)

Linear

12.
How much does it cost to rent the Karaoke machine for 3 days?
How much does it cost to rent the Karaoke machine for 3 days?
a)
$50
b)
$100
c)
$150
d)
$175
e)

$75

13.

Portions of a "step" function

a)
may be connected
b)
cannot be connected
c)
may be connected or may not be connected
d)

None of these

14.
Which of functions represents the graph?

Which of functions represents the graph?

a)
Which of functions represents the graph?
b)
Which of functions represents the graph?
c)
Which of functions represents the graph?
d)
Which of functions represents the graph?
e)

None of these

15.
Postage rates on envelopes are a great example of step functions . There is a fixed price for a certain range of weights and…

Postage rates on envelopes are a great example of step functions. There is a fixed price for a certain range of weights and then another fixed price for another range of weights, etc. Below is the graph of one such price structure.


According to this graph, what would be the postage rate on a letter weighing 1.5 ounces?

a)

$0.50

b)

$0.70

c)

$1.00

d)

$1.10

e)

$0.90

WaygroundAnswer Key

Lesson 1-3: Piecewise Functions Practice

Total questions: 15

1.
d) 1
2.
c)
3.
b) x ≥ 0
4.
c) 3
5.
d) 17
6.
a) 4
7.
a)

-2 < x ≤ 1

8.
a)

0

9.
a) -3
10.
c) 4
11.
c)

Step Function

12.
b) $100
13.
b) cannot be connected
14.
c)
15.
b)

$0.70

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FAQs

What does this piecewise functions worksheet cover?

This Grade 10 worksheet uses 15 multiple-choice questions to practice evaluating piecewise functions, identifying domain restrictions for individual graph pieces, and interpreting graphs. It also asks students to recognize step functions, select a function represented by a graph, and apply step-function reasoning to rental and postage-rate examples.

How can I use this worksheet to teach piecewise and step functions?

Use the evaluation questions first to model how students choose the rule that applies to a given input, including values such as f(0), f(4), and f(-2). Then discuss the graph-based domain restrictions and step-function items, asking students to explain how open or closed endpoints and horizontal sections determine which rule or value applies. Finish with the karaoke rental and postage examples to connect interval-based rules to pricing situations.

What mistakes should I watch for on this piecewise functions worksheet?

Watch for students substituting an input into the wrong piece, especially when a domain restriction includes one endpoint but excludes another. Students may also confuse a function’s value at an endpoint, misread graph coordinates such as f(-3), or treat a step function as continuous rather than as separate constant portions. In the application questions, check that students identify the correct price interval before selecting an amount.

How do I assign and grade this piecewise functions worksheet?

You can assign this worksheet as a printable PDF or as a digital quiz on Wayground. It includes a complete answer key for checking the 15 multiple-choice responses, and printable submissions can be graded by scanning student work with the Wayground for Teachers app. The printable format can also support schools that are reducing screen time.

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

In the worksheet’s Advanced Settings, adjust font spacing or choose a larger font size so the function notation, graph prompts, and multiple-choice options are easier to read. You can also apply 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 comprehensive collection of free printable worksheets and practice problems across all 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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