1. y x Lesson 3.7 Objective: Graphing Absolute Value Functions.
EQ: How do you transform an absolute value function?
Solve & Graph #1:
y = |x|
Step 1 – create a table x y
Step 2 – plot the ordered pairs
Step 3 – draw the V-shaped graph x y
Domain:
All Real Numbers
Range:
Y ≥ 0

2. A basic function used as building blocks for more complicated functions.
Parent function:
Absolute value function:
A function that contains an absolute value equation. The Parent function for an absolute value function is y=|x|
Vertex:
The point where the graph changes direction. The VERTEX of the parent absolute value function y= |x| is (0,0) or the origin.
Translating graphs:
The rigid movement of a function vertically or horizontally.

3. y x y x g(x) = |x – 2| The graph translated 2 units to the right x
g(x) -5 -3 -1 1 2 3 7 5 3 2 1 1
How did this function change? x y
g(x) = |x + 2|
The graph translated 2 units to the left x
g(x) -3 -2 -1 1 2 3 1 1 2 3 4 5
How did this function change?

4. y x y x f(x) = | x | - 2 x The graph translated 2 units down f(x)
f(x) -3 -2 -1 1 2 3 1 -1 -2 -1 1
How did this function change? x y
The graph translated 2 units up
f(x) = | x | + 2 x
f(x) -3 -2 -1 1 2 3 5 4 3 2 3 4 5
How did this function change?

5. y x y x The graph narrowed / stretched g(x) = 2 | x | x g(x)
g(x) -3 -2 -1 1 2 3 6 4 2 2 4 6
How did this function change?
Vertical Stretch.
By a factor of 2 x y
g(x) = ½ | x |
The graph grew wider / shrank x
g(x) -4 -2 -1 1 2 4 2 1 .5 .5 1 2
How did this function change?
Vertical Shrink.
By a factor of ½

6. y x x f(x) = - | x | f(x) How did this function change?
f(x) -3 -2 -1 1 2 3 -3 -2 -1 -1 -2 -3
How did this function change?
The graph reflected over the x-axis

7. y x y x f(x) = |2 x | x f(x) How did this function change? x
f(x) -3 -2 -1 1 2 3 6 4 2 2 4 6
How did this function change?
Horizontal shrink by factor of ½.
f(x) = | ½ x | x y x
f(x) -4 -2 -1 1 2 4 2 1 .5 .5 1 2
How did this function change?
Horizontal stretch by a factor of 2