Free Printable WorksheetMathGrade 8Math Curriculum8.F.A.3

8.101 Recognizing Linear and Nonlinear Functions Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Grade 8 Math worksheet provides structured practice on 8.101 Recognizing Linear and Nonlinear Functions. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

8.101 Recognizing Linear and Nonlinear Functions - Which function is linear and which is nonlinear based on the representation? (CCSS 8.F.A.3; CA 8.F.A.3; MA 8.F.A.3)

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Grade 8

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related 8.101 Recognizing Linear and Nonlinear Functions skill assessments:

Problem 1Difficulty: Hard
Which option lists one linear function and one nonlinear function in that order?
Ay = 5x - 1; y = x2 + 4
By = 2x; y = 3x + 2
Cperimeter of a square as a function of side length; cost of x identical pencils
Darea of a square as a function of side length; y = 1/x
Solution & Explanation:In option A, y = 5x - 1 is linear and y = x2 + 4 is nonlinear. The other options do not match the requested order of one linear function followed by one nonlinear function.
Problem 2Difficulty: Hard
Which claim is correct?
AA function is linear whenever the outputs get bigger.
BA function is nonlinear whenever the slope is negative.
CA function is linear only when it has a constant rate of change and a straight-line graph.
DA function is nonlinear only when its outputs are fractions.
Solution & Explanation:The defining features of a linear function are a constant rate of change and a straight-line graph. The other claims use incorrect rules.
Problem 3Difficulty: Hard
Function A follows y = -3x + 2. Function B doubles every day. Function C has points (0, 1), (2, 5), (4, 9), and (6, 13). Which functions are linear?
AFunction A only
BFunction B only
CFunctions A and C only
DFunctions B and C only
Solution & Explanation:Function A is linear from its equation. Function C is linear because equal x-changes of 2 give equal y-changes of 4. Function B is nonlinear because it doubles.

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Frequently Asked Questions

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Grade 8 Math students. It aligns with educational standard 8.F.A.3 (Primary standard selected for prompt fields: CCSS 8.F.A.3. Skill statement: Which function is linear and which is nonlinear based on the representation? Associated standards listed with this skill: CCSS 8.F.A.3; CA 8.F.A.3; MA 8.F.A.3. Use this embedded wording as the best available supporting standard description for this workflow.).

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