Free Printable WorksheetMathAlgebra IIMath CurriculumF-BF.1c

ALG2.88 Decomposing Composite Functions Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Algebra II Math worksheet provides structured practice on ALG2.88 Decomposing Composite Functions. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG2.88 Decomposing Composite Functions - Identify component functions within a composition and select the statement that explains how the inner function changes inputs before the outer function acts. Associated source-listed standards: CCSS F-BF.1c; CA CCSSM F-BF.1c; MA 2017 F-BF.1c; NY NGLS F-BF.1c; 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 ALG2.88 Decomposing Composite Functions skill assessments:

Problem 1Difficulty: Mastery
For the decomposition h(x) = f(g(x)) with h(x) = ln((x - 2)2/(x + 1)) and f(x) = ln(x), what value does the inner function assign to x = 5?
Solution & Explanation:The inner function is g(x) = (x - 2)2/(x + 1). At x = 5 this becomes 9/6 = 3/2.
Problem 2Difficulty: Mastery
Suppose h(x) = cbrt(9 - 2x) + 1 is written as f(g(x)) and f(x) = cbrt(x) + 1. Find g(4).
Solution & Explanation:The inner function is g(x) = 9 - 2x. Then g(4) = 9 - 8 = 1.
Problem 3Difficulty: Mastery
Let h(x) = abs(1/(2x + 1)). If h(x) = f(g(x)) with f(x) = abs(x), what is g(3)?
Solution & Explanation:The inner function is g(x) = 1/(2x + 1). Evaluating at x = 3 gives g(3) = 1/7.

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Frequently Asked Questions

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QIs this ALG2.88 Decomposing Composite Functions worksheet free for teachers and homeschoolers?

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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-BF.1c (Identify component functions within a composition and select the statement that explains how the inner function changes inputs before the outer function acts. Associated source-listed standards: CCSS F-BF.1c; CA CCSSM F-BF.1c; MA 2017 F-BF.1c; NY NGLS F-BF.1c; TX TEKS Algebra II: §111.40.).

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