Free Printable WorksheetMathPre-CalculusMath CurriculumSMP 1,2,4,5,8

Pre CAL.189 Identify Removable, Jump, and Infinite Discontinuities 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.189 Identify Removable, Jump, and Infinite Discontinuities. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

Pre-CAL.189 Identify Removable, Jump, and Infinite Discontinuities - Primary standard selected for prompt fields in this prompt cell: SMP 1,2,4,5,8. Skill statement in this prompt cell: Given a graph or equation, determine the discontinuity type at a point and select the correct description of the limit behavior there. Associated standards listed with this skill in this prompt cell: SMP 1,2,4,5,8; VA MA.CF.2-3; NCTM CCHS. 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.189 Identify Removable, Jump, and Infinite Discontinuities skill assessments:

Problem 1Difficulty: Mastery

For f(x) = (x² - 6x + 9)/(x³ - 27), which statement correctly describes the discontinuity at x = 3?

AJump discontinuity; the one-sided limits are finite but unequal at x=3.

BInfinite discontinuity; the denominator creates a vertical asymptote at x=3 after all cancellation.

CRemovable discontinuity; lim x->3 f(x) = 0, but the original function is undefined at x=3.

DContinuous at x=3; f(3)=0 and the limit equals 0.

Solution & Explanation:The numerator is (x - 3)² and the denominator is (x - 3)(x² + 3x + 9). After canceling one factor, the limit is 0/(27) = 0, so the discontinuity is removable.

Problem 2Difficulty: Mastery

For f(x) = (x + 3)/(x² - 9), which statement correctly describes the discontinuity at x = -3?

ARemovable discontinuity; the two-sided limit is -1/6, but f(-3) is undefined.

BJump discontinuity; the one-sided limits are finite but unequal at x=-3.

CInfinite discontinuity; f(x) grows without bound near x=-3.

DContinuous at x=-3; the function value and the two-sided limit both equal -1/6.

Solution & Explanation:The denominator is (x + 3)(x - 3). Cancel x + 3, then evaluate 1/(x - 3) at x = -3 to get -1/6. The original expression is undefined at -3, so the discontinuity is removable.

Problem 3Difficulty: Mastery

For f(x) = (x² - 49)/(x - 7), which statement correctly describes the discontinuity at x = 7?

AJump discontinuity; the one-sided limits are finite but unequal at x=7.

BInfinite discontinuity; f(x) grows without bound near x=7.

CRemovable discontinuity; the two-sided limit is 14, but f(7) is undefined.

DContinuous at x=7; the function value and the two-sided limit both equal 14.

Solution & Explanation:Factor x² - 49 as (x - 7)(x + 7). After canceling x - 7, the nearby values follow x + 7, which approaches 14 at x = 7.

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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 SMP 1,2,4,5,8 (Primary standard selected for prompt fields in this prompt cell: SMP 1,2,4,5,8. Skill statement in this prompt cell: Given a graph or equation, determine the discontinuity type at a point and select the correct description of the limit behavior there. Associated standards listed with this skill in this prompt cell: SMP 1,2,4,5,8; VA MA.CF.2-3; NCTM CCHS. Use this prompt-provided wording as the supporting standard description for this workflow.).