Free Printable WorksheetMathAlgebra IIMath CurriculumF-IF.9

ALG2.67 Comparing Functions Across Representations Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Algebra II Math worksheet provides structured practice on ALG2.67 Comparing Functions Across Representations. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG2.67 Comparing Functions Across Representations - Select the correct comparison between properties of two functions represented in different ways and decide which grows faster or has larger values over an interval. Associated source-listed standards: CCSS F-IF.9; CA CCSSM F-IF.9; MA 2017 F-IF.9; NY NGLS F-IF.9; TX TEKS Algebra II: §111.40.

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

Algebra II

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 ALG2.67 Comparing Functions Across Representations skill assessments:

Problem 1Difficulty: Mastery

Function A is f(x) = (x - 2)² + 3. Function B is shown in the table: x: 0, 1, 2, 3, 4; g(x): 0, 2, 4, 6, 8. On the interval from x = 0 to x = 4, which statement is true?

AFunction A has the smaller minimum on the interval, and Function A is larger at x = 4

BFunction B has the smaller minimum on the interval, and Function B is larger at x = 4

CThe functions have the same minimum on the interval, but Function B is larger at x = 4

DFunction B has the smaller minimum on the interval, but Function A is larger at x = 4

Solution & Explanation:Function A has minimum value 3 on the interval, while Function B has minimum value 0. At x = 4, Function A is 7 and Function B is 8. So Function B has the smaller minimum and the larger value at x = 4.

Problem 2Difficulty: Mastery

Function A is defined recursively by a(0) = 0 and a(n) = a(n - 1) + 6. Function B is g(x) = 4x + 5. Which statement correctly compares the functions?

AFunction A has the smaller initial value, but the greater average rate of change

BFunction B has the smaller initial value, but the greater average rate of change

CFunction A and Function B have the same initial value and same rate of change

DFunction A starts larger, and Function B changes faster

Solution & Explanation:Function A starts at 0 and has constant rate 6. Function B starts at 5 and has constant rate 4. So Function A starts smaller but changes faster.

Problem 3Difficulty: Mastery

Function A is f(x) = 2x² - 3. Function B is shown in the table: x: 0, 1, 2, 3; g(x): -3, 2, 7, 12. Which statement is true?

AThe functions are equal only at x = 0, and Function A is larger by x = 3

BThe functions are equal at x = 0 and x = 3, and Function B is larger in between

CFunction B is always larger than Function A on the listed x-values

DFunction A starts larger, but Function B becomes larger by x = 3

Solution & Explanation:Function A has values -3, -1, 5, and 15. Function B has values -3, 2, 7, and 12. They are equal only at x = 0, and by x = 3 Function A is larger.

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Algebra II Math students. It aligns with educational standard F-IF.9 (Select the correct comparison between properties of two functions represented in different ways and decide which grows faster or has larger values over an interval. Associated source-listed standards: CCSS F-IF.9; CA CCSSM F-IF.9; MA 2017 F-IF.9; NY NGLS F-IF.9; TX TEKS Algebra II: §111.40.).