Free Printable WorksheetMathAlgebra IIMath CurriculumF-IF.7

ALG2.144 Graphing Radical 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 ALG2.144 Graphing Radical Functions. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG2.144 Graphing Radical Functions - CCSS F-IF.7. Skill statement: Select the graph that matches square root, cube root, and other radical functions; identify domain and range; and describe transformations. Associated standards: CCSS F-IF.7; F-BF.3; CA CCSSM F-IF.7; F-BF.3; MA 2017 F-IF.7; F-BF.3; NY NGLS F-IF.7; F-BF.3; 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 ALG2.144 Graphing Radical Functions skill assessments:

Problem 1Difficulty: Mastery
Which statement is always true for f(x) = a cbrt(x - h) + k when a is not 0?
AThe domain is [h, infinity), and the range is [k, infinity)
BThe graph has a maximum at (h, k)
CThe graph has a vertical asymptote at x = h
DThe domain and range are all real numbers, and the center point is (h, k)
Solution & Explanation:Cube root transformations keep all real x-values and y-values. The shift parameters h and k locate the center point.
Problem 2Difficulty: Mastery
Which function has domain [-3, 5] and range [2, 6]?
Af(x) = sqrt(25 - (x - 1)2) + 2
Bf(x) = sqrt(16 - (x + 1)2) + 2
Cf(x) = sqrt(16 - (x - 1)2) + 2
Df(x) = cbrt(x - 1) + 2
Solution & Explanation:The expression 16 - (x - 1)2 gives a radius of 4 centered at x = 1, so the domain is [-3, 5]. The square root ranges from 0 to 4, then +2 gives [2, 6].
Problem 3Difficulty: Mastery
What are the domain and range of f(x) = sqrt(25 - (x - 1)2) + 3?
ADomain [1, 6], range [0, 5]
BDomain [-4, 6], range [3, 8]
CDomain (-infinity, infinity), range [3, 8]
DDomain [-5, 5], range [0, 8]
Solution & Explanation:The radicand requires (x - 1)2 <= 25, so -5 <= x - 1 <= 5 and -4 <= x <= 6. The square root ranges from 0 to 5, then +3 gives 3 to 8.

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Frequently Asked Questions

Common questions about printing, using, and solving this worksheet

QHow do I download and print this ALG2.144 Graphing Radical Functions worksheet?

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QIs this ALG2.144 Graphing Radical 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-IF.7 (CCSS F-IF.7. Skill statement: Select the graph that matches square root, cube root, and other radical functions; identify domain and range; and describe transformations. Associated standards: CCSS F-IF.7; F-BF.3; CA CCSSM F-IF.7; F-BF.3; MA 2017 F-IF.7; F-BF.3; NY NGLS F-IF.7; F-BF.3; TX TEKS Algebra II: §111.40.).

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