Free Printable WorksheetMathAlgebra IIMath CurriculumF-LE.4

ALG2.173 Identifying Valid Log Inputs Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Algebra II Math worksheet provides structured practice on ALG2.173 Identifying Valid Log Inputs. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG2.173 Identifying Valid Log Inputs - Primary standard selected for prompt fields in this prompt cell: CCSS F-LE.4. Skill statement in this prompt cell: Identify when log arguments must be positive and apply this restriction when graphing or solving. Associated standards listed with this skill in this prompt cell: CCSS F-LE.4; F-IF.2; CA CCSSM F-LE.4; F-IF.2; MA 2017 F-LE.4; F-IF.2; NY NGLS F-LE.4; F-IF.2; TX TEKS Algebra II: §111.40. Use this prompt-provided wording as the supporting standard description for this workflow.

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 ALG2.173 Identifying Valid Log Inputs skill assessments:

Problem 1Difficulty: Mastery
What is the domain of log((x2 - 4)/(x2 - 9))?
A(-infinity, -3) U (-2, 2) U (3, infinity)
B(-3, -2) U (2, 3)
Cx != -3, -2, 2, and 3
D(-2, 2) only
Solution & Explanation:Use a sign chart with critical values -3, -2, 2, and 3. The quotient is positive on (-infinity, -3), (-2, 2), and (3, infinity).
Problem 2Difficulty: Mastery
When graphing y = log_2(5 - x) + 4, which statement correctly describes the boundary and side of the graph?
Avertical asymptote x = 5; graph to the left
Bvertical asymptote x = 5; graph to the right
Cvertical asymptote x = -5; graph to the right
Dhorizontal asymptote y = 5; graph above it
Solution & Explanation:The argument 5 - x must be positive, so x < 5. The boundary x = 5 is the vertical asymptote, and the graph lies to its left.
Problem 3Difficulty: Mastery
The graph of y = log((x + 1)/(x - 3)) is shown. Which intervals contain graph branches?
A-1 < x < 3
Bx < -1 or x > 3
Cx > -1
Dall real x except -1 and 3
Solution & Explanation:The quotient (x + 1)/(x - 3) is positive when numerator and denominator have the same sign. That occurs for x < -1 or x > 3.

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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 Algebra II Math students. It aligns with educational standard F-LE.4 (Primary standard selected for prompt fields in this prompt cell: CCSS F-LE.4. Skill statement in this prompt cell: Identify when log arguments must be positive and apply this restriction when graphing or solving. Associated standards listed with this skill in this prompt cell: CCSS F-LE.4; F-IF.2; CA CCSSM F-LE.4; F-IF.2; MA 2017 F-LE.4; F-IF.2; NY NGLS F-LE.4; F-IF.2; TX TEKS Algebra II: §111.40. Use this prompt-provided wording as the supporting standard description for this workflow.).

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