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).
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