Free Printable WorksheetMathPre-CalculusMath CurriculumPre-CAL.47

Pre CAL.47 Identify Removable and Infinite Discontinuities in Rational Functions 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.47 Identify Removable and Infinite Discontinuities in Rational Functions. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

Pre-CAL.47 Identify Removable and Infinite Discontinuities in Rational Functions - Identify Removable and Infinite Discontinuities in Rational Functions

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.47 Identify Removable and Infinite Discontinuities in Rational Functions skill assessments:

Problem 1Difficulty: Mastery

f(x) = (2x⁴ + 32x³ + 156x² + 224x + 98) / (x⁴ + 2x³ - 83x² - 84x + 1764) Which option correctly lists ALL holes and vertical asymptotes? (Answer A, B, C, or D.)

AHoles: -7, -8; Vertical asymptotes: 6

BHoles: -7; Vertical asymptotes: none

CHoles: -7; Vertical asymptotes: 6

DHoles: none; Vertical asymptotes: 6

Solution & Explanation:Factor numerator and denominator. Any factor that cancels creates a hole at its zero(s). Any factor that remains in the denominator creates vertical asymptotes at its zero(s).

Problem 2Difficulty: Mastery

f(x) = (x⁴ + 18x³ + 103x² + 198x + 112) / (x² + 8x + 7) Find the x-value of the removable discontinuity (hole).

Solution & Explanation:Factor the numerator and denominator and cancel any common factor. The canceled factor equals 0 at x = -1, so x = -1 is a hole (removable discontinuity).

Problem 3Difficulty: Mastery

f(x) = (-x² - 10x - 9) / ((x - 8)(x + 1)²) The function has more than one vertical asymptote. What is the smaller x-value of a vertical asymptote?

Solution & Explanation:Vertical asymptotes are the x-values that make the simplified denominator 0. Among those values, the smaller one is x = -1.

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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 Pre-CAL.47 (Identify Removable and Infinite Discontinuities in Rational Functions).