Function Transformations and Stretch/Compression

vertical stretch, translation left 3

• ½f(x + 3)

• 4f(x - 3)

• 4f(x) + 3

• 4f(x + 3)

translation up 1

• f(x) + 1

• f(x - 1)

• f(x) - 1

• f(x + 1)

reflection over y-axis, shift right 1

• f(-x - 1)

• -f(x + 1)

• -f(x) - 1

• -f(x - 1)

horizontal compression

• g(x) = 3f(x)

• g(x) = ½f(x)

• g(x) = f(¼x)

• g(x) = f(5x)

vertical reflection, horizontal stretch

• g(x) = ½f(-x)

• g(x) = -f(¼x)

• g(x) = -3f(x)

• g(x) = -f(4x)

Describe the transformations from the original parent function f(x) = x².

g(x) = 5x² + 2

• Vertical Stretch of 5

  Down 2

• Vertical Compression of 5

  Up 2

• Vertical Stretch of 5

  Up 2

• Vertical Compression of 5

  Down 2

Describe the parent graph transformation

• vertical stretch by 1/2, left 1, down 3

• horizontal stretch by 1/2, right 1, down 3

• vertical compression by 1/2, left 1, down 3

• horizontal compression by 1/2, right 1, down 3

What transformations has the function undergone?

• reflect over y, vertical compression by 2, right 5, up 1

• reflect over x, horizontal compression by 2, left 5, up 1

• reflect over x, vertical stretch by 2, right 5, up 1

• reflect over y, horizontal stretch by -2, right 5, up 1

Describe the transformation that is applied to the parent function.

f(x) = 3 Ix+8I

• Vertically Stretches by 3, Shifts left 8

• Vertically Stretches by 3, Shifts right 8

• Vertically Stretches by 3, Shifts up 8

• Vertically Stretches by 3, Shifts down 8

• X axis reflection

• Y axis reflection

• Left 1

• Vertical stretch by 2

• Horizontal compression by 1/2