Free Printable WorksheetMathAlgebra IIMath CurriculumF-BF.3

ALG2.77 Transformations of Function Graphs Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Algebra II Math worksheet provides structured practice on ALG2.77 Transformations of Function Graphs. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG2.77 Transformations of Function Graphs - Select the statement that best describes and apply translations, reflections, and stretches or compressions to create new functions from parent functions. Associated source-listed standards: CCSS F-BF.3; CA CCSSM F-BF.3; MA 2017 F-BF.3; NY NGLS F-BF.3; TX TEKS Algebra II: §111.40.

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

Algebra II

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 ALG2.77 Transformations of Function Graphs skill assessments:

Problem 1Difficulty: Mastery
Which transformed function has endpoint (5, -2), is reflected across the x-axis, and is vertically stretched by factor 3 compared with y = sqrt(x)?
Ay = 3sqrt(x - 5) - 2
By = -3sqrt(x - 5) - 2
Cy = -3sqrt(x + 5) - 2
Dy = -sqrt(3(x - 5)) - 2
Solution & Explanation:An endpoint at (5, -2) means x - 5 inside the square root and -2 outside. Reflection across the x-axis and a vertical stretch by 3 give the factor -3 outside.
Problem 2Difficulty: Mastery
Which function is a horizontal stretch by factor 3 of y = log_2(x), followed by a shift right 1 unit?
Ay = log_2((x - 1)/3)
By = log_2(3(x - 1))
Cy = log_2(x/3) + 1
Dy = 3log_2(x - 1)
Solution & Explanation:A horizontal stretch by 3 replaces x with x/3. After also shifting right 1, the input becomes (x - 1)/3.
Problem 3Difficulty: Mastery
If (-1, 2) and (3, -4) lie on y = f(x), which pair of points lies on y = -f(x - 2) + 1?
A(1, -1) and (5, 5)
B(-3, -1) and (1, 5)
C(1, 3) and (5, -5)
D(1, 1) and (5, -3)
Solution & Explanation:The x - 2 shifts the graph right 2, so the x-values become 1 and 5. Then the y-values transform by -y + 1, giving -2 + 1 = -1 and 4 + 1 = 5.

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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 Algebra II Math students. It aligns with educational standard F-BF.3 (Select the statement that best describes and apply translations, reflections, and stretches or compressions to create new functions from parent functions. Associated source-listed standards: CCSS F-BF.3; CA CCSSM F-BF.3; MA 2017 F-BF.3; NY NGLS F-BF.3; TX TEKS Algebra II: §111.40.).

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