Free Printable WorksheetMathPre-CalculusMath CurriculumHSA-SSE.1-3

Pre CAL.48 Determine Horizontal and Vertical Asymptotes Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Pre-Calculus Math worksheet provides structured practice on Pre CAL.48 Determine Horizontal and Vertical Asymptotes. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

Pre-CAL.48 Determine Horizontal and Vertical Asymptotes - Primary standard selected for prompt fields in this prompt cell: CCSS HSA-SSE.1-3. Skill statement in this prompt cell: Given a rational function, identify the correct vertical and horizontal (or oblique) asymptotes and select the graph behavior that matches them. Associated standards listed with this skill in this prompt cell: CCSS HSA-SSE.1-3; CCSS HSA-APR.1-7(+); CCSS HSF-IF.7c-7d,8a; CCSS HSA-REI.11; SMP 1,2,7,8; AP Precalculus CED Unit 1; TX §111.42(c)(5)(B-H); FL MA.912.AR.6.3-6.6, MA.912.AR.8.3; VA MA.CF.1. 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

Pre-Calculus

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 Pre CAL.48 Determine Horizontal and Vertical Asymptotes skill assessments:

Problem 1Difficulty: Mastery
For B(x) = (x4 - 81)/(x3 - 9x), which statement is correct?
Avertical asymptote x = 0; holes at x = -3 and x = 3; slant asymptote y = x
Bvertical asymptotes x = -3, x = 0, and x = 3; horizontal asymptote y = 1
Cvertical asymptote x = 3; holes at x = -3 and x = 0; slant asymptote y = x
Dno vertical asymptote; holes at x = -3, x = 0, and x = 3; slant asymptote y = x
Solution & Explanation:Factor x4 - 81 as (x - 3)(x + 3)(x2 + 9), and factor the denominator as x(x - 3)(x + 3). The factors x - 3 and x + 3 cancel, so x = -3 and x = 3 are holes. The remaining denominator x gives vertical asymptote x = 0, and the slant asymptote is y = x.
Problem 2Difficulty: Mastery
For A(x) = (4x3 - 12x2 + x - 3)/(2x2 - 6x), which statement is correct?
Avertical asymptote x = 0; hole at x = 3; slant asymptote y = 2x
Bvertical asymptote x = 3; hole at x = 0; slant asymptote y = 2x
Cvertical asymptotes x = 0 and x = 3; horizontal asymptote y = 2
Dno vertical asymptote; holes at x = 0 and x = 3; slant asymptote y = 2x
Solution & Explanation:Factor the numerator by grouping as (x - 3)(4x2 + 1), and the denominator as 2x(x - 3). The x - 3 factor cancels, creating a hole at x = 3. The remaining denominator x gives vertical asymptote x = 0, and (4x2 + 1)/(2x) has slant asymptote y = 2x.
Problem 3Difficulty: Mastery
Use the graph shown. Which description best matches the function?
Avertical asymptote x = 0; horizontal asymptote y = -2; hole at x = 3
Bvertical asymptote x = 3; horizontal asymptote y = -2; hole at x = 0
Cvertical asymptote x = -2; horizontal asymptote y = 0; hole at x = 3
Dno vertical asymptote; horizontal asymptote y = -2; holes at x = 0 and x = 3
Solution & Explanation:The dashed vertical line is at x = 0, the dashed horizontal line is at y = -2, and the open circle marks a removable hole at 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 Pre-Calculus Math students. It aligns with educational standard HSA-SSE.1-3 (Primary standard selected for prompt fields in this prompt cell: CCSS HSA-SSE.1-3. Skill statement in this prompt cell: Given a rational function, identify the correct vertical and horizontal (or oblique) asymptotes and select the graph behavior that matches them. Associated standards listed with this skill in this prompt cell: CCSS HSA-SSE.1-3; CCSS HSA-APR.1-7(+); CCSS HSF-IF.7c-7d,8a; CCSS HSA-REI.11; SMP 1,2,7,8; AP Precalculus CED Unit 1; TX §111.42(c)(5)(B-H); FL MA.912.AR.6.3-6.6, MA.912.AR.8.3; VA MA.CF.1. Use this prompt-provided wording as the supporting standard description for this workflow.).

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