1. What you will learn today
1. How to graph an absolute value function
2. How to determine the equation of an absolute value graph

2. Absolute Value Functions
Use an x/y table to graph the following:
y = |x|
x y
Objective: 2.8 Absolute Value Functions

3. Graphing Calculator Fun
Let’s see how the graphs change as we add things to the equation.
y = 2|x|
y = -2|x|
y = |x – 2|
y = |x| + 2
Objective: 2.8 Absolute Value Functions

4. In Summary
The graph of y = a|x – h| + k has the following characteristics:
1. The graph has vertex at (h, k) and is symmetric in the line x = h.
2. The graph is V-shaped. It opens up if a>0 and down if a<0.
3. The graph is wider than the graph of y = |x| if |a| < 1. The graph is narrower than the graph of y = |x| if |a| > 1.
Objective: 2.8 Absolute Value Functions

5. Graphing an Absolute Value Function
Graph y = |x+2| + 3
Safest way – Get the vertex from the equation. Use an x/y table.
Objective: 2.8 Absolute Value Functions

6. You Try
Graph y = |x – 2| - 3
Objective: 2.8 Absolute Value Functions

7. Another Example - Negative
Graph: y = -|x – 1 | + 1
Objective: 2.8 Absolute Value Functions

8. You Try
Graph y = -|x +2| + 3
Objective: 2.8 Absolute Value Functions

9. Example – Writing an Absolute Value Function
Page 123. The vertex of the graph is (0, -3), so the equation has the form y = a|x – h| + k. Another point on the graph is (2, 1).
1. Substitute
y = a|x – 0| + -3
2. Substitute the point (2, 1) for x and y in the equation and solve for a.
3. The equation is:
Objective: 2.8 Absolute Value Functions

10. You Try Write an equation for the graph shown:
Objective: 2.8 Absolute Value Functions

11. A “Real World” Example Y = -1.4|x – 2.5| + 3.5
The front of a camping tent can be modeled by the function:
Y = -1.4|x – 2.5| + 3.5
Where x and y are measured in feet and the x-axis represents the ground. Graph the function and interpret the domain and range of the function in the given context.
Objective: 2.8 Absolute Value Functions

12. Homework
Page 126, all, 20, 22, 26, 34, 36
How to use the graphing calculator.
Objective: 2.8 Absolute Value Functions