Function Transformations

Translations

100

Describe the translation.

f(x)=x-4

Shift Right 4 OR Shift Down 4

200

Describe the translation.

f(x)=(x-2)^2+4

Shift Right 2 and Up 4

300

Describe the translation.

f(x)=(x+2)^2

Shift Left 2

400

Describe the translation.

f(x)=|x-2|+3

Shift Right 2 and Up 3

500

Describe the translation.

g(x)=f(x-4)+7

Shift Right 4 and Up 7

Dilations & Reflections

100

Name the transformation.

f(x)=2x^2

Stretch vertically by a factor of 2.

200

Name the transformation.

f(x)=1/3|x|

Vertical shrink by a factor of 1/3.

300

Name the transformation.

f(x)=-2|x|

Reflection over the x-axis and vertical stretch by a factor of 2. 

400

Name the transformation.

f(x)=-2x^2

Reflection over the x-axis and vertical stretch by a factor of 2.

500

Name the transformations.

f(x)=2(-x)^2

Vertical stretch by a factor of 2 and reflect over the y-axis.

Mixed

100

Name the transformations.

f(x)=(x-2)^2+5

Shift right 2, up 5

200

Name the transformations.

f(x)=2(x-1)^2

Vertical stretch by a factor of 2, horizontal shift right 1

300

Describe the transformations.

f(x)=-1/4x^2-6

Reflection over the x-axis, vertical shrink by a factor of 1/4, and vertical shift down 6.

400

Name the transformations.

f(x)=2sqrt(x)-9

Vertical stretch by a factor of 2 and vertical shift down 9.

500

Name the transformations.

g(x)=1/5f(x)-8

Vertical shrink by a factor of 1/5 and a vertical shift down 8.

Where's my Parent?

100

Name the Parent Function.

f(x)=2|x+12|

Absolute Value

f(x)=|x|

200

Name the Parent Function.

f(x)=3/2x^2+1

Quadratic

f(x)=x^2

300

Name the Parent Function.

f(x)=(x-7)^2+pi

Quadratic.

f(x)=x^2

400

Name the Parent Function.

f(x)=1/4(x-1)^3-5/2

Cubic.

f(x)=x^3

500

Name the Parent Function.

g(x)=sin(x-pi)

Sine / Trigonometric.

g(x)=sin(x)