Function Transformations

A Function Dilation...

• Shifts a graph from left to right

• Mirrors a graph over the x or y axis

• Stretches or Compresses a graph towards or away from the x or y axis

This represents a ____________ of a function

• Translation

• Reflection

• Dilation

To create this Left Translation of the original graph (in purple), the new function rule will be...

-f(x) will do what to a function?

• Dilate it by compressing it.

• Reflect it over the x-axis

• Shift it to the left

Which translations occurred to the original function (in purple)?

• Shift to the left 3 spaces; Shift upwards 4 spaces

• Shift down 4 spaces; Shift to the left 3 spaces

• Shift to the left 4 spaces; Shift upwards 3 spaces

What function rule represents these Translations?

(Shift to the left 4 spaces; Shift upwards 3 spaces)

• f(x) = 2(x - 4)² - 3

• f(x) = 2(x - 4)² + 3

• f(x) = 2(x + 4)² - 3

• f(x) = 2(x + 4)² + 3

A function Reflection...

• Stretches or Compresses a graph towards or away from the x or y-axis

• Shifts a graph from left to right or up and down

• Creates a mirror image of the a graph over an axis

Tags

CCSS.HSF.BF.B.3

f(x + k) will...

• Shift a graph upwards

• Shift a graph downwards

• Shift a graph to the right

• Shift a graph to the left

In a Reflection over the x-axis, a function's outputs will...

• remain the same

• turn into their opposites

Tags

CCSS.HSF.BF.B.3

The original base-function that hasn't been transformed can be called a _________ _________ (2 words).

(a)