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

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)

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.

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) (-3,2) (-1,2)

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)

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

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

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