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Precalculus practice

Function Transformations

Map key points across shifts, reflections, stretches, and compressions for seven common parent-function families.

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Apply transformations to parent key points in the correct inside/outside order. Preserve real-domain restrictions and classify parity only when requested.

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These worksheets pair exact algebra with labeled graph scales, explicit domains, bounded intervals, and model assumptions. The generated teacher key uses the same resolved task document as the student preview.

Learning objective

What this activity builds

Apply inside and outside transformations in the correct order while preserving domains, branches, and parity facts.

Worked example

Describe g(x)=-2f((x-3)/2)+1.

Horizontal stretch by 2, right 3; reflect across the x-axis, vertical stretch by 2, up 1.

Inside changes map x-coordinates; outside changes map y-coordinates.

Teaching notes

Make the practice count

  • Map points rather than guessing curve shape.
  • Track square-root endpoints and reciprocal asymptotes.
  • Classify parity from f(-x), not appearance alone.

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Math SheetNameScoreTeacherDateFunction TransformationsApply transformations to parent key points in the correct inside/outside order. Preserve real-domain restrictions and classify parity only when requested.1. Write an equation for the shown transformation of the linear parent. Also classify the transformed function g as even, odd, or neither.Assumptions: The plotted curve samples the real parent function between its mapped key points.Parent pointMapped point(-2, -2)(-2, -4)(-1, -1)(-1, -5)(0, 0)(0, -6)-7-11-3.5-5.5003.55.57112. Complete the mapped-point table and graph g(x) = -2 f((x-0)/0.5) from the cube-root parent. Also classify the transformed function g as even, odd, orneither.Assumptions: The plotted curve samples the real parent function between its mapped key points.Parent pointMapped point(-8, -2)(-1, -1)(0, 0)-7-7-3.5-3.5003.53.577Show exact work and preserve every stated domain restriction.math-sheet.comPage 1 of 3
Math SheetNameScoreTeacherDateFunction TransformationsApply transformations to parent key points in the correct inside/outside order. Preserve real-domain restrictions and classify parity only when requested.3. Complete the mapped-point table and graph g(x) = 1 f((x+3)/1) + 4 from the square-root parent. Also classify the transformed function g as even, odd, orneither.Assumptions: The transformed real domain begins at the mapped endpoint.Parent pointMapped point(0, 0)(1, 1)(4, 2)-7-8-3.5-4003.54784. Describe the transformations from the quadratic parent to g(x) = -2 f((x+3)/-1) - 1. Also classify the transformed function g as even, odd, or neither.Assumptions: The plotted curve samples the real parent function between its mapped key points.Parent pointMapped point(-2, 4)(-1, -9)(-1, 1)(-2, -3)(0, 0)(-3, -1)-8-34-4-1700417834Show exact work and preserve every stated domain restriction.math-sheet.comPage 2 of 3
Math SheetNameScoreTeacherDateFunction TransformationsApply transformations to parent key points in the correct inside/outside order. Preserve real-domain restrictions and classify parity only when requested.5. Complete the mapped-point table and graph g(x) = 1 f((x+4)/1) - 2 from the cube-root parent. Also classify the transformed function g as even, odd, orneither.Assumptions: The plotted curve samples the real parent function between its mapped key points.Parent pointMapped point(-8, -2)(-1, -1)(0, 0)-13-7-6.5-3.5006.53.51376. Describe the transformations from the square-root parent to g(x) = 0.5 f((x-0)/2). Also classify the transformed function g as even, odd, or neither.Assumptions: The transformed real domain begins at the mapped endpoint.Parent pointMapped point(0, 0)(0, 0)(1, 1)(2, 0.5)(4, 2)(8, 1)-19-7-9.5-3.5009.53.5197Show exact work and preserve every stated domain restriction.math-sheet.comPage 3 of 3

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