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

Pre CAL.22 Write Equations from Transformed Graphs 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.22 Write Equations from Transformed Graphs. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

Pre-CAL.22 Write Equations from Transformed Graphs - Primary standard selected for prompt fields in this prompt cell: CCSS HSF-IF.1-6,9. Skill statement in this prompt cell: Given a graph and a parent function, determine the correct transformed equation that matches the graph. 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.22 Write Equations from Transformed Graphs skill assessments:

Problem 1Difficulty: Mastery
The graph shown is a transformation of the parent function y = x3. The cubic's center point is (0, 4), the graph decreases from left to right, and the labeled point (1, 1) is on the graph. Which equation matches the graph?
Ay = 3*x3 + 4
By = -3*(x - 4)3
Cy = -0.333*x3 + 4
Dy = -3*x3 + 4
Solution & Explanation:Use y = a*x3 + 4 because the center is (0, 4). Substituting (1, 1) gives 1 = a + 4, so a = -3.
Problem 2Difficulty: Mastery
The graph shown is a transformation of the parent function y = cos(x). The cosine wave has amplitude 1.5, midline y = 2, period 6pi, and a maximum at x = 0. Which equation matches the graph?
Ay = 1.5*cos(3*x) + 2
By = 3*cos((1/3)*x) + 2
Cy = 1.5*cos((1/3)*x) + 2
Dy = -1.5*cos((1/3)*x) + 2
Solution & Explanation:Period 6pi means b = 2pi/(6pi) = 1/3. A maximum at x = 0 keeps the cosine coefficient positive, with amplitude 1.5 and midline 2.
Problem 3Difficulty: Mastery
The graph shown is a transformation of the parent function y = log2(x). The logarithmic graph has vertical asymptote x = 5 and x-intercept at x = 7. Which equation matches the graph?
Ay = log2(x + 5) - 1
By = log2(x - 5) - 1
Cy = log2(x - 5) + 1
Dy = -log2(x - 5) - 1
Solution & Explanation:Asymptote x = 5 gives x - 5. At the x-intercept x = 7, log2(2) = 1, so subtracting 1 makes y = 0.

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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 graph and a parent function, determine the correct transformed equation that matches the graph. 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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