2.6 Families of Functions

1. Translations2. Stretches, Shrinks and

Reflections

2) Stretches and Shrinks

• Stretching a rubber band vertically makes it longer

• Releasing or shrinking it makes it wider

• Stretching and shrinking a graph is the same idea…

• What does it look like?

2) Stretches and Shrinks

Shrink

Graph is SHORTER,

WIDER

Stretch

Graph is TALLER,

NARROWER

2) Stretches

For stretches,

y = a|x|

a > 1

2) Stretches

For stretches,

y = a|x|

a > 1

a is SLOPE

2) Stretches

Example 1:Graph y = 2|x|.

2) Stretches

Example 1:Graph y = 2|x|.

y = 2|x|

Slope =

Vertex =

2) Stretches

Example 1:Graph y = 2|x|.

y = 2|x|

Slope = 2

Vertex = (0, 0)

2) Stretches

Example 1:Graph y = 2|x|.

Step 1:

Plot the vertex

2) Stretches

Example 1:Graph y = 2|x|.

Step 1:

Plot the vertex

Step 2:

Use slope to plot points

2) Stretches

Example 1:Graph y = 2|x|.

Step 1:

Plot the vertex

Step 2:

Use slope to plot points

2) Stretches

Example 1:Graph y = 2|x|.

Step 1:

Plot the vertex

Step 2:

Use slope to plot points

2) Stretches

Example 1:Graph y = 2|x|.

Step 1:

Plot the vertex

Step 2:

Use slope to plot points

2) Stretches

Example 2:Write an equation for the graph below.

2) Stretches

Example 2:Write an equation for the graph below.

Vertex =

Slope =

2) Stretches

Example 2:Write an equation for the graph below.

Vertex = (0, 0)

Slope = 4, -4

2) Stretches

Example 2:Write an equation for the graph below.

Vertex = (0, 0)

Slope = 4

y = -4|x|

2) Shrinks…kind of like you stepped

on the graph…

2) Shrinks

For shrinks,

y = a|x|

0 < a < 1

2) Shrinks

Example 1:Draw the graph of y = -0.5|x|.

2) Shrinks

Example 1:Draw the graph of y = -0.5|x|.

slope = 0.5

= 1

2

vertex = (0, 0)

opens DOWN

2) Shrinks

Example 1:Draw the graph of y = -0.5|x|.

2) Shrinks

Example 1:Draw the graph of y = -0.5|x|.

Slope = 1

2

2) Shrinks

Example 1:Draw the graph of y = -0.5|x|.

Slope = 1

2

2) Shrinks

Example 1:Draw the graph of y = -0.5|x|.

Slope = 1

2

2) Shrinks

Example 2: Graph y = -0.75|x – 2| + 2

Example 2:

Graph y = -0.75|x – 2| + 2

slope = 0.75 shift RIGHT 2 shift UP 2

= 3 4

2) Shrinks

Opens DOWN

2) Shrinks

Example 2: Graph y = -0.75|x – 2| + 2

Vertex = (2, 2)

Slope = 3

4

2) Shrinks

Example 2: Graph y = -0.75|x – 2| + 2

Vertex = (2, 2)

Slope = 3

4

2) Shrinks

Example 2: Graph y = -0.75|x – 2| + 2

Vertex = (2, 2)

Slope = 3

4

2) Shrinks

Example 2: Graph y = -0.75|x – 2| + 2

Vertex = (2, 2)

Slope = 3

4

Homework

p.98 #17, 19, 22, 25, 34, 36, 43-45, 49

QUIZ: 2.5-2.7 Tuesday Sept 29

TEST: Chapter 2 Friday Oct 2(I know you have a Literature test…but trust me, it’s better this way).