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Families of Functions. Objective: I can understand transformations of functions. Vocabulary. Parent Function Simplest form in a set of functions. Transformation : Change in the size or position of a function Translation : Moves a function horizontally or vertically Reflection:

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families of functions

Families of Functions

Objective:

I can understand transformations of functions.

vocabulary
Vocabulary

Parent Function

  • Simplest form in a set of functions.

Transformation:

  • Change in the size or position of a function

Translation:

  • Moves a function horizontally or vertically

Reflection:

  • Reflects a function across a line of reflection

Dilation:

  • Changes a function size
translations
Set your calculator window to:

Graph

Graph

Graph

Translations

Vertical Translation: k units

Up: Down:

translations1
Graph

Graph

Graph

Translations

Horizontal Translation, h units

Left: Right:

reflections
Graph

Graph

Graph

Reflections

Reflections:

Across x-axis

Across y-axis

dilations
Graph

Graph

Graph

Dilations

Dilations: Vertical

stretchcompression

transformation of f x
Transformation of f(x)

Translation: Horizontal (k > 0)

Translation: Vertical (k > 0)

Up k units

Right h units

Down k units

Left h units

Reflection

Dilation: Vertical by a factor of a

Across x-axis

Stretch:

Across y-axis

Compression:

combining transformations
Combining Transformations

Find g(x) when f(x) is stretched by a factor of 0.5 and reflected across the y-axis.

Find g(x) when f(x) is translated 3 units up.

Find g(x) when f(x) is translated 2 units left.

Pg. 104 #10-33