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Comparing Functions Algebra I - Printable Mathematics Worksheets - Wayground

Comparing Functions Algebra I

12 questions

9th - 12th Grade

Mathematics

Comparing Functions Algebra I is a free printable mathematics worksheet for Grades 9–12 that develops students’ ability to compare linear functions across equations, tables, graphs, and real-world situations. The 12 questions ask students to identify and compare initial values, y-intercepts, x-intercepts, and rates of change, including a multiple-select item in which they compare rates of change from several representations. Students apply these skills to contexts such as party-planning fees, weight loss, and pizza-delivery salaries, then determine which function changes faster, starts higher, or reaches a target value. The worksheet helps learners connect symbolic, graphical, and tabular representations instead of relying on a single calculation method. It is available as a free printable worksheet with a complete answer key, making it useful for Algebra I practice, review, or an assessment of students’ function-comparison skills.

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Worksheets

Comparing Functions Algebra I

Total questions: 12

Name
Class
Date
1.

Janet is planning her sweet sixteen birthday party. She must decide which party coordinator she should use so that she spends the least amount of money possible. Each coordinator charges an initial fee for their services, plus an additional fee depending on the number of guests that attend the party. Each coordinator's rates are shown in the image.


Which coordinator charges the greatest initial fee?

a)

Coordinator A

b)

Coordinator B

c)

Coordinator C

d)

Coordinator D

2.

Janet is planning her sweet sixteen birthday party. She must decide which party coordinator she should use so that she spends the least amount of money possible. Each coordinator charges an initial fee for their services, plus an additional fee depending on the number of guests that attend the party. Each coordinator's rates are shown in the image.


Which coordinator charges the greatest fee per guest?

a)

Coordinator A

b)

Coordinator B

c)

Coordinator C

d)

Coordinator D

3.

Jasmine compared the x-intercept of f(x) = 2x – 8 to the x-intercept of the function shown in the table.


What is the value of the larger x-intercept of the two functions?

a)

-8

b)

-2

c)

4

d)

16

4.

Which function has a greater rate of change than the function A in the table?

a)

 y=35x−5\ y=\frac{3}{5}x-5

b)

y=37x+2y=\frac{3}{7}x+2

c)

y=1+12xy=1+\frac{1}{2}x

d)

y=−1+14xy=-1+\frac{1}{4}x

5.

Which functions have a rate of change that is greater than the function shown in the graph? Select ALL that apply.

a)

f(x)=12x−5f\left(x\right)=\frac{1}{2}x-5

b)

g(x)=x+6g\left(x\right)=x+6

c)

h(x)=34x−9h\left(x\right)=\frac{3}{4}x-9

d)

j(x)=14x+8j\left(x\right)=\frac{1}{4}x+8

e)

k(x)=xk\left(x\right)=x

6.

Equation A: y = 3x - 1

Equation B: -2y - 6x = 2

Which equation has a greater y intercept?

a)

Equation A

b)

Equation B

c)

They have the same Y intercept

7.

Function A is represented by the equation y = 4x - 2. Function B is represented by the table.


Which of these functions has the greater rate of change?

a)

Function A. It's rate of change is -2.

b)

Function A. It's rate of change is 4.

c)

Function B. It's rate of change is 2.

d)

Function B. It's rate of change is 6.

8.

Function A is represented by the equation. y=23x+5y=\frac{2}{3}x+5  

Function B is represented by the graph. What is the y-intercept of each function?

a)

Function A

y-int= 23\frac{2}{3}

Function B

y-int=-1

b)

Function A

y-int=5

Function B

y-int=-1

c)

Function A

y-int=5

Function B

y-int=2

d)

Function A

y-int=2

Function B

y-int= 32\frac{3}{2}

9.
Who weighed more at the beginning of the show?
a)

Valerie

b)

Oscar

c)

Mrs. Conte

d)

They weighed the same

10.
Who is losing weight faster?
a)

Valerie

b)

Oscar

c)

Mrs. Conte

d)

They are losing the same amount of weight

11.

Which pizza place pays the best salary per pizza delivered? How many pizzas would the pizzeria need to deliver to make at least $ 100 dollars in one night? Write the equation of each Pizzeria salary scale.

a)

Bombino's

21 pizzas

f(x)= 56x+2.5

b)

Little Squeezers

20 pizzas

f(x)= 3x+48

c)

Little Squeezers

15 pizzas

f(x)= 48+9x

d)

Bombino's

18 pizzas

f(x)= 2.5x+56

12.

Function A is represented by the equation:

4x−4y=−164x-4y=-16  

Function B is represented by the table.

Who has the smallest rate of change

a)

Function A

4

b)

Function B

9

c)

Function A

1

d)

Function B

2

e)

They have the same rate of change

Answer Key

Comparing Functions Algebra I

Total questions: 12

1.
b)

Coordinator B

2.
d)

Coordinator D

3.
c)

4

4.
a)

 y=35x−5\ y=\frac{3}{5}x-5

5.
b)

g(x)=x+6g\left(x\right)=x+6

, c)

h(x)=34x−9h\left(x\right)=\frac{3}{4}x-9

, e)

k(x)=xk\left(x\right)=x

6.
c)

They have the same Y intercept

7.
b)

Function A. It's rate of change is 4.

8.
b)

Function A

y-int=5

Function B

y-int=-1

9.
b)

Oscar

10.
a)

Valerie

11.
b)

Little Squeezers

20 pizzas

f(x)= 3x+48

12.
c)

Function A

1

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FAQs

What does the Comparing Functions Algebra I worksheet cover?

This worksheet helps students compare linear functions by identifying initial values, x-intercepts, y-intercepts, and rates of change from equations, tables, graphs, and applied situations. Its 12 items, including 11 multiple-choice questions and one multiple-select question, require students to determine which function starts higher, changes faster, or meets a stated condition.

How can I use this worksheet to teach students to compare linear functions?

Introduce rate of change and intercepts separately, then model how the same feature appears in an equation, table, or graph. Use the party-coordinator and pizza-salary items to connect slope and initial value to real costs or earnings, and ask students to explain which part of each representation supports their choice before completing the comparison questions independently.

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

Students may confuse the y-intercept or initial fee with the rate of change per guest, especially in the party-planning and pizza-delivery contexts. They may also read a coefficient incorrectly, compare only the vertical position of graph lines, or select a function with a larger intercept when the question asks for the greater rate of change. In the multiple-select item, check that students evaluate every option rather than choosing only one function.

How do I assign and grade this Comparing Functions Algebra I worksheet?

You can assign it as a printable PDF or as a digital quiz on Wayground, with the complete answer key included for checking responses to the equation, table, graph, and real-world comparison items. For printable submissions, scan student work with the Wayground for Teachers app to support grading and review.

How can I differentiate this worksheet for my students?

In the worksheet’s Advanced Settings, adjust font spacing or font size to make the equations, tables, graph-based prompts, and answer choices easier to navigate. You can also enable a dyslexia-friendly font or translate the worksheet into another language when those options support access to the function-comparison tasks.

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

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