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

Pre CAL.12 Using Technology for Function Exploration 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.12 Using Technology for Function Exploration. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

Pre-CAL.12 Using Technology for Function Exploration - Primary standard selected for prompt fields in this prompt cell: CCSS HSF-IF.1-6,9. Skill statement in this prompt cell: Given technology outputs (graph windows, trace values, tables, or solver results), determine which settings or conclusions are correct and identify errors caused by poor window choices. 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.12 Using Technology for Function Exploration skill assessments:

Problem 1Difficulty: Mastery
A student explores f(x)=0.1x3-5x. A table with step 5 shows f(-10)=-50, f(-5)=12.5, f(0)=0, f(5)=-12.5, and f(10)=50. Which final technology report is most defensible?
AThe table proves the only zero is x=0.
BThe graph and solver should be used with a window around x=-8 to 8 because additional zeros are near x=-7.07.
CThe function has no turning points because the table alternates signs.
DThe x-window should be 100 to 200 because all roots are there.
Solution & Explanation:Solving 0.1x3-5x=0 gives x(0.1x2-5)=0, so x=0 and x=-sqrt(50), about -7.07. A step of 5 misses those noninteger zeros.
Problem 2Difficulty: Mastery
A graph view suggests two curves intersect near x=100, but the lines are thick. A table gives f(99.9)-g(99.9)=-0.03 and f(100.1)-g(100.1)=0.03. What is the best conclusion?
AThere is likely an intersection near x=100, but a solver or smaller table step should refine the estimate.
BThe intersection is exactly x=100 because the graph looks that way.
CThere is no intersection because neither table value is 0.
DThe graph window proves infinitely many intersections.
Solution & Explanation:The sign of f-g changes between 99.9 and 100.1, so an intersection is likely in that interval. A solver can refine the approximate x-value.
Problem 3Difficulty: Mastery
A solver for x4=16 returns x=2 when the starting guess is positive. What should be checked for real solutions?
Ax=-2 is also a real solution, so another guess or the graph should be used.
BThere are no real solutions because fourth powers are always negative.
Cx=0 must be the other solution.
DOnly positive solutions can satisfy fourth-power equations.
Solution & Explanation:Both 24 and (-2)4 equal 16. A positive starting guess may return only the positive solution.

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Frequently Asked Questions

Common questions about printing, using, and solving this worksheet

QHow do I download and print this Pre CAL.12 Using Technology for Function Exploration worksheet?

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QIs this Pre CAL.12 Using Technology for Function Exploration worksheet free for teachers and homeschoolers?

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QCan students practice Pre CAL.12 Using Technology for Function Exploration online with instant feedback?

Yes! In addition to this printable worksheet, students can practice Pre CAL.12 Using Technology for Function Exploration interactively on our platform with automated grading, instant score tracking, and detailed step-by-step solutions.

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 technology outputs (graph windows, trace values, tables, or solver results), determine which settings or conclusions are correct and identify errors caused by poor window choices. 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.).

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