Summary of Transformations Worksheet showing function transformations and their effects on graphs and domains/ranges.

Summary of transformations for functions, including vertical and horizontal translations, reflections, and stretches/compressions, with examples and domain/range changes.

PNG 298×386 10.3 KB Free · Personal Use

Quality Assured by Worksheets Library Team

Reviewed for educational accuracy and age-appropriateness

ID: #284138

✨ Generate New Worksheet

⭐

Show Answer Key & Explanations Step-by-step solution for: Transforming Functions Worksheet - Fill Online, Printable ...

▼

a. 2f(x - 5)
Stretch vertically by a factor of 2.
Shift right 5.
Domain: [-4+5, 1+5] = [1, 6]
Range: [2*(-3), 2*4] = [-6, 8]

b. -f(2x) + 7
Reflect in x-axis.
Shrink horizontally by a factor of 1/2 (or compress by factor 2).
Shift up 7.
Domain: [-4/2, 1/2] = [-2, 0.5]
Range: [-4+7, 3+7] = [3, 10]

c. 3f(½x + 4) - 2
Stretch vertically by a factor of 3.
Stretch horizontally by a factor of 2.
Shift left 8 (since ½(x + 8) = ½x + 4).
Shift down 2.
Domain: [2*(-4-4), 2*(1-4)]? Wait, correct: for ½x + 4, set u = ½x + 4, so x = 2(u - 4). When u in [-4,1], x in [2(-4-4), 2(1-4)] = [2(-8), 2(-3)] = [-16, -6]. Actually, to get input for f, set ½x + 4 ∈ [-4,1]. So ½x ∈ [-8,-3], so x ∈ [-16,-6].
Range: [3*(-3)-2, 3*4-2] = [-9-2, 12-2] = [-11, 10]

Parent Tip: Review the logic above to help your child master the concept of function transformations worksheet.

Print Download

How to use

Click Print to open a print-ready version directly in your browser, or use Download to save the file to your device. The ⭐ Answer button generates an AI answer key instantly - useful for teachers who need a quick reference. Need a different version? Our AI Worksheet Generator lets you create a custom worksheet on any topic in seconds.

Related worksheets: function transformations worksheet