1. 4.6.2 – Graphing Absolute Value Functions

2. Recall, a function f(x) = |x| is consider an absolute value function
What shape are the graphs for absolute value functions?

3. All are in the shape of a “v”
Some properties will determine
if the graph opens up, or down,
and if it is wide or narrow

4. Up or Down?
For an absolute value function f(x) = a|x|, the a value will tell us if it opens up, or down
If a > 0, then the graph opens up
If a < 0, then the graph opens down

5. Narrow or Wide?
The a value in f(x) = a|x| also helps us determine if the graph is narrow, or wide, compared to f(x) = |x|
If |a| > 1, then the graph is narrower than y = |x|
If |a| < 1, then the graph is wider than y = |x|

6. How to graph?
To graph the absolute value function f(x) = |x|, we will choose a positive x value to substitute
From yesterday, what is one key property of the graphs of absolute value functions?
Use the point of symmetry for a second point

7. Example. Graph the function f(x) = 2|x|.
Up or down?

8. Example. Graph the function f(x) = -3|x|.
Up or down?

9. Example. Graph the function f(x) = -4|x|.
Up or down?

10. Using your Calculators
Take out your graphing calculators
We will take a look at the a value and compare when we start to change it

11. Assignment
Pg. 208
21-29 odd, odd, 59