Absolute Value Functions

1. Absolute Value Functions What is an absolute value function? How is an absolute value graph graphed, written, and interpreted?

2. The absolute value of x is defined by: The graph of this piecewise function consists of two rays, is V-shaped and opens up. The corner point of the graph, called the vertex, occurs at the origin. (-2,2) (2,2)

3. Graphing Absolute Value Functions The graph of y = a|x−h|+k has the following characteristics. • The graph has vertex (h,k) and is symmetric in the line x=h. • The graph is V-shaped. It opens up if a>0 and down if a<0. • 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.

4. Graph y = −|x+2| +3 • Plot the vertex. • Then plot another point on the graph. • Use symmetry to plot a third point. • Connect the points in a V shaped graph. (-2,3) (-1,2) (-3,2)

5. Write an equation of the graph shown. The vertex of the graph is (0,-3). y = a|x−0|+(−3) or y=a|x|−3. Find the value of a using (2,1). 1=2a−3, a = 2 Equation of the graph is y=2|x|−3 (2,1) (0,-3)

6. Interpreting an Absolute Value Function Open your book to page 124, example 3.

7. What is an absolute value function? A function with an absolute value variable. • How is an absolute value graph graphed, written, and interpreted? An absolute value graph is a piecewise function consisting of two rays forming a V shape. The generic equation is: y = aI x−h I + k

8. Assignment 2.8 Page 125, 12-25,35-37, 49, 50