Free Printable WorksheetMathAlgebra IIMath CurriculumF-IF.7d

ALG2.136 Determining Horizontal and Slant Asymptotes Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Algebra II Math worksheet provides structured practice on ALG2.136 Determining Horizontal and Slant Asymptotes. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG2.136 Determining Horizontal and Slant Asymptotes - Primary standard selected for prompt fields in this prompt cell: CCSS F-IF.7d. Skill statement in this prompt cell: Select the correct use of degree comparisons and polynomial division to determine horizontal or slant asymptotes for rational functions. Associated standards listed with this skill in this prompt cell: CCSS F-IF.7d; A-APR.6; CA CCSSM F-IF.7d; A-APR.6; MA 2017 F-IF.7d; A-APR.6; NY NGLS F-IF.7d; A-APR.6; 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 ALG2.136 Determining Horizontal and Slant Asymptotes skill assessments:

Problem 1Difficulty: Mastery

A practice set includes rational functions with degree pairs (2, 5), (4, 4), (5, 4), and (6, 3). Which strategy correctly identifies horizontal and slant asymptotes?

AFirst divide every rational function, then decide whether the quotient is useful.

BAlways use the leading-coefficient ratio because it is faster.

CAlways set the denominator equal to 0 before looking for end behavior.

DFirst compare degrees, then divide only for the function whose numerator degree is exactly one greater than the denominator degree.

Solution & Explanation:Degree comparison sorts the cases: (2,5) gives y = 0, (4,4) gives a leading-coefficient-ratio horizontal asymptote, (5,4) requires division for a slant asymptote, and (6,3) gives neither horizontal nor slant.

Problem 2Difficulty: Mastery

Match each function to its end-behavior conclusion: A(x) = (-6x² + 1)/(2x² + 3), B(x) = (2x² + 3x + 4)/(x + 1), C(x) = (x⁴ + x)/(x² + 1).

AA: y = 0; B: y = 2; C: y = x²

BA: y = -3; B: no slant; C: y = 0

CA: y = -3; B: y = 2x + 1; C: no horizontal or slant asymptote

DA: slant y = -3x; B: horizontal y = 2; C: slant y = x²

Solution & Explanation:A has equal degrees, so y = -6/2 = -3. B has degrees 2 and 1, so division gives quotient 2x + 1 and a slant asymptote. C has degree difference 2, so it has neither a horizontal nor a slant asymptote.

Problem 3Difficulty: Mastery

For f(x) = (x² - 3x + 10)/(2x + 2), which conclusion is correct after polynomial division?

AThe horizontal asymptote is y = 1/2.

BThe slant asymptote is y = (1/2)x - 2.

CThe slant asymptote is y = 2x - 1.

DThere is no slant asymptote because the denominator coefficient is 2.

Solution & Explanation:The numerator degree is 2 and the denominator degree is 1, so divide. The quotient is (1/2)x - 2 with remainder 14, and the remainder term approaches 0. The slant asymptote is y = (1/2)x - 2.

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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 correct use of degree comparisons and polynomial division to determine horizontal or slant asymptotes for rational functions. Associated standards listed with this skill in this prompt cell: CCSS F-IF.7d; A-APR.6; CA CCSSM F-IF.7d; A-APR.6; MA 2017 F-IF.7d; A-APR.6; NY NGLS F-IF.7d; A-APR.6; TX TEKS Algebra II: §111.40.).