Free Printable WorksheetMathAlgebra IIMath CurriculumF-IF.7d

ALG2.129 Graphing Rational 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 ALG2.129 Graphing Rational Functions. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG2.129 Graphing Rational Functions - Primary standard selected for prompt fields in this prompt cell: CCSS F-IF.7d. Skill statement in this prompt cell: Select the graph that matches rational functions and identify intercepts, vertical and horizontal (or slant) asymptotes, holes, and end behavior. Associated standards listed with this skill in this prompt cell: CCSS F-IF.7d; A-REI.11; CA CCSSM F-IF.7d; A-REI.11; MA 2017 F-IF.7d; A-REI.11; NY NGLS F-IF.7d; A-REI.11; 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 ALG2.129 Graphing Rational Functions skill assessments:

Problem 1Difficulty: Mastery
Use the graph options in the image. Which graph matches f(x) = ((x - 1)(x + 2))/((x + 2)(x + 5))?
AGraph A: hole at (-5, -1), vertical asymptote x = -2, horizontal asymptote y = 1
BGraph B: no hole, vertical asymptotes x = -2 and x = -5, horizontal asymptote y = 0
CGraph C: hole at (-2, 0), vertical asymptote x = 1, horizontal asymptote y = -1
DGraph D: hole at (-2, -1), vertical asymptote x = -5, horizontal asymptote y = 1
Solution & Explanation:The factor x + 2 cancels, creating a hole at (-2, -1). The remaining function (x - 1)/(x + 5) has vertical asymptote x = -5, horizontal asymptote y = 1, and x-intercept (1, 0). Graph D matches.
Problem 2Difficulty: Mastery
For f(x) = (3x2 + 2x - 1)/(x + 1), which description matches the graph?
AVertical asymptote x = -1 and slant asymptote y = 3x - 1
BHorizontal asymptote y = 3 and x-intercept (-1, 0)
CLine y = 3x - 1 with a hole at (-1, -4)
DLine y = x + 1 with a hole at (1/3, 0)
Solution & Explanation:Factor the numerator as (3x - 1)(x + 1). The common factor cancels, so the graph is y = 3x - 1 with a hole at x = -1. The hole is (-1, -4).
Problem 3Difficulty: Mastery
For f(x) = (x2 + 8x + 15)/(x + 3), what is the y-coordinate of the hole?
Solution & Explanation:Factor the numerator as (x + 3)(x + 5). After canceling x + 3, the simplified graph is y = x + 5. At x = -3, the hole has y = 2.

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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-IF.7d (Primary standard selected for prompt fields in this prompt cell: CCSS F-IF.7d. Skill statement in this prompt cell: Select the graph that matches rational functions and identify intercepts, vertical and horizontal (or slant) asymptotes, holes, and end behavior. Associated standards listed with this skill in this prompt cell: CCSS F-IF.7d; A-REI.11; CA CCSSM F-IF.7d; A-REI.11; MA 2017 F-IF.7d; A-REI.11; NY NGLS F-IF.7d; A-REI.11; TX TEKS Algebra II: §111.40. Use this prompt-provided wording as the supporting standard description for this workflow.).

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