Free Printable WorksheetMathPre-CalculusMath CurriculumHSF-IF.1-6,9

Pre CAL.19 Identify Relative Extrema and End Behavior 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.19 Identify Relative Extrema and End Behavior. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

Pre-CAL.19 Identify Relative Extrema and End Behavior - Primary standard selected for prompt fields in this prompt cell: CCSS HSF-IF.1-6,9. Skill statement in this prompt cell: Given a function graph or equation, identify relative maxima and minima and select the statement that correctly describes end behavior. Associated standards listed with this skill in this prompt cell: CCSS HSF-IF.1-6,9; CCSS HSF-BF.1-4; CCSS HSA-CED.1-4; SMP 1,2,4,5,7; AP Precalculus CED Units 1-3; TX §111.42(c)(2)(A-L); FL MA.912.F.1.4, MA.912.F.1.7, MA.912.F.3.3-3.9, MA.912.AR.9.10; VA MA.CF.1, MA.FR.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.19 Identify Relative Extrema and End Behavior skill assessments:

Problem 1Difficulty: Mastery

For f(x) = |x² - 4|, which statement correctly describes the relative extrema and end behavior?

ARelative maxima at (-2, 0) and (2, 0) and relative minimum at (0, 4); as x -> -infinity, f(x) -> -infinity, and as x -> infinity, f(x) -> -infinity.

BRelative minima at (-2, 0) and (2, 0) and relative maximum at (0, 4); as x -> -infinity, f(x) -> -infinity, and as x -> infinity, f(x) -> infinity.

CNo relative extrema; as x -> -infinity, f(x) -> infinity, and as x -> infinity, f(x) -> infinity.

DRelative minima at (-2, 0) and (2, 0) and relative maximum at (0, 4); as x -> -infinity, f(x) -> infinity, and as x -> infinity, f(x) -> infinity.

Solution & Explanation:The absolute value makes the zeros of x² - 4 into sharp relative minima at x = -2 and x = 2. Between them the graph peaks at (0, 4), and both ends rise.

Problem 2Difficulty: Mastery

Let g(x) = -x² for x <= 0 and g(x) = (x - 2)² - 4 for x > 0. Which statement matches the function?

ARelative minimum at (0, 0) and relative maximum at (2, -4); as x -> -infinity, f(x) -> -infinity, and as x -> infinity, f(x) -> infinity.

BRelative maximum at (0, 0) and relative minimum at (2, -4); as x -> -infinity, f(x) -> infinity, and as x -> infinity, f(x) -> -infinity.

CRelative maximum at (0, 0) and relative minimum at (2, -4); as x -> -infinity, f(x) -> -infinity, and as x -> infinity, f(x) -> infinity.

DNo relative extrema; as x -> -infinity, f(x) -> -infinity, and as x -> infinity, f(x) -> infinity.

Solution & Explanation:Near x = 0, values on both sides are below 0, so (0, 0) is a relative maximum. The right-hand parabola has a vertex at (2, -4), and the ends go down on the left and up on the right.

Problem 3Difficulty: Mastery

Let f(x) = x² for x <= 1 and f(x) = -x + 2 for x > 1. Which statement is correct?

ARelative maximum at (0, 0) and relative minimum at (1, 1); as x -> -infinity, f(x) -> infinity, and as x -> infinity, f(x) -> -infinity.

BRelative minimum at (0, 0) and relative maximum at (1, 1); as x -> -infinity, f(x) -> infinity, and as x -> infinity, f(x) -> -infinity.

CRelative minimum at (0, 0) and relative maximum at (1, 1); as x -> -infinity, f(x) -> -infinity, and as x -> infinity, f(x) -> infinity.

DNo relative extrema; as x -> -infinity, f(x) -> infinity, and as x -> infinity, f(x) -> -infinity.

Solution & Explanation:The parabola has a local low at (0, 0), and the joined graph has a local high at (1, 1). As x goes left the x² piece rises, while as x goes right the line falls.

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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 HSF-IF.1-6,9 (Primary standard selected for prompt fields in this prompt cell: CCSS HSF-IF.1-6,9. Skill statement in this prompt cell: Given a function graph or equation, identify relative maxima and minima and select the statement that correctly describes end behavior. Associated standards listed with this skill in this prompt cell: CCSS HSF-IF.1-6,9; CCSS HSF-BF.1-4; CCSS HSA-CED.1-4; SMP 1,2,4,5,7; AP Precalculus CED Units 1-3; TX §111.42(c)(2)(A-L); FL MA.912.F.1.4, MA.912.F.1.7, MA.912.F.3.3-3.9, MA.912.AR.9.10; VA MA.CF.1, MA.FR.1. Use this prompt-provided wording as the supporting standard description for this workflow.).