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

Pre CAL.34 Graphs of Polynomial Functions 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.34 Graphs of Polynomial Functions and End Behavior. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

Pre-CAL.34 Graphs of Polynomial Functions and End Behavior - Primary standard selected for prompt fields in this prompt cell: CCSS HSA-SSE.1-3. Skill statement in this prompt cell: Given a polynomial function or its factored form, select the graph that matches its end behavior and zeros and identify key features such as intercepts and turning points. 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 Section 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.34 Graphs of Polynomial Functions and End Behavior skill assessments:

Problem 1Difficulty: Mastery
Which description matches f(x)=-0.5(x+4)(x-2)2(x-5)3?
Aboth ends fall; crosses at x=-4; touches at x=2; flattened crossing at x=5
Bleft end rises and right end falls; touches at x=-4 and x=2; crosses at x=5
Cboth ends rise; crosses at x=-4 and x=5; touches at x=2
Dboth ends fall; touches at all three zeros
Solution & Explanation:The degree is 6 with a negative leading coefficient, so both ends fall. The simple factor crosses at -4, the squared factor touches at 2, and the cubic factor crosses with flattening at 5.
Problem 2Difficulty: Mastery
A graph falls to the left, rises to the right, touches at x=-3, crosses at x=0, touches at x=2, and passes through (1,12). If f(x)=a(x+3)2*x*(x-2)2, what is a? Enter a decimal.
Solution & Explanation:Substitute x=1 and y=12: 12=a(4)2(1)(-1)2=16a, so a=0.75. The positive coefficient also matches the required odd-degree end behavior.
Problem 3Difficulty: Mastery
If a polynomial graph only touches the x-axis at x=7 instead of crossing there, what must be true about the exponent on the factor (x-7)?
AIt must be a positive even exponent.
BIt must be a positive odd exponent.
CIt must be exactly 1.
DIt must be negative.
Solution & Explanation:Touching and turning at a zero is associated with even multiplicity, so the factor (x-7) must have a positive even exponent.

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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 polynomial function or its factored form, select the graph that matches its end behavior and zeros and identify key features such as intercepts and turning points. 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 Section 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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