1. Graphing Absolute Value Functions

2. Vocabulary
The function f(x) = |x| is an absolute value function.

3. The graph of this function is V-shaped, and opens up.
To the left of
x=0 the line is
y = -x
To the right of
x = 0 the line is
y = x
Notice that the graph is symmetric over the y-axis because for
every point (x,y) on the graph, the point (-x,y) is also on it.

4. Vocabulary
The highest or lowest point on the graph of an absolute value function is called the vertex.
An axis of symmetry of the graph of a function is a vertical line that divides the graph into mirror images.
An absolute value graph has one axis of symmetry that passes through the vertex.

5. Absolute Value Function
Vertex
Axis of Symmetry

6. Vocabulary
The zeros of a function f(x) are the values of x that make the value of f(x) zero.
On this graph, the zeros are:
x = -3 and x = 3.
f(x) = |x| - 3

7. y = -a |x – h| + k *Remember that (h, k) is your vertex*
Reflection across the x-axis
Vertical Translation
Vertical Stretch a > 1 (makes it narrower) OR Vertical Compression 0 < a < 1 (makes it wider)
Horizontal Translation
(opposite of h)
*Remember that (h, k) is your vertex*

8. Example 1 Describe the transformations: y = 3 |x + 2| - 3

9. Example 2 (You will need graph paper.)
Graph y = -2 |x + 3| + 2.
What is the vertex?
What are the intercepts?
What are the zeros?

10. Example 3
Graph y = - ½ |x – 1| - 2

11. Example 4
Write a function for the graph shown.

12. Example 5
Write a function for the graph shown.