1. 2-7 Absolute Value Functions and Graphs
Apply rules for transformations by graphing absolute value functions.
2-7 Absolute Value Functions and Graphs

2. Absolute Value Function
V-shaped graph that opens up or down
Up when positive, down when negative
Parent function: y = |x|
Axis of symmetry is the vertical axis through the middle of the graph.
Has a single maximum point OR minimum point called the vertex.

3. Translation Shift of a graph horizontally, vertically, or both.
Same size and shape, different position

4. Try it. Create a table and sketch the graph of the following:
y = |x| + 2
y = |x| - 3
What do you notice?

5. Vertical Translation Start with the graph of y = |x|
y = |x| + k translates the graph up
y = |x| - k translates the graph down

6. Try this. Create a table and sketch the graph of the following:
y = |x + 3|
y = |x – 1|
What do you notice?

7. Horizontal Translation
Start with the graph of y = |x|
y = |x + h| translates the graph to the left
y = |x – h| translates the graph to the right.

8. Vertical Stretch and Compression
Use a table to graph 𝑦=3|𝑥|.
What do you notice?
Now try: 𝑦= 1 3 |𝑥|
When the coefficient is greater than 1 we have a vertical stretch (making the graph narrower)
Between 0 and 1 we have a compression (making the graph wider)

9. General Form 𝑦=𝑎 𝑥−ℎ +𝑘 |𝑎| creates a stretch or compression
You can find the a-value by finding the slope of the branch to the right.
ℎ creates a horizontal translation
𝑘 creates a vertical translation
The vertex is located at (h,k)
The axis of symmetry is the line x = h

10. Writing Absolute Value Functions
What is the equation of the absolute value function?
Vertex: (-1,4)
So h = -1 and k = 4
Find the slope of the branch to the right
− 1 3 is your a-value
Substitute into the general form
𝑦=− 1 3 𝑥+1 +4

11. Assignment
Odds p.111 #13-33