3 4 Absolute Value Functions Absolute Value is

3. 4 Absolute Value Functions

Absolute Value is defined by:

The graph of this piecewise function consists of 2 rays, is V-shaped and opens up. To the left of x=0 the line is y = -x To the right of x = 0 the line is y=x Notice that the graph is symmetric in the y-axis because every point (x, y) on the graph, the point (-x, y) is also on it.

y = a |x - h| + k �Vertex is at (h, k) & is symmetrical in the line x=h �V-shaped �If a < 0 the graph opens down (a is negative) �If a > 0 the graph opens up (a is positive) �The graph is wider if |a| < 1 (fraction < 1) �The graph is narrower if |a| > 1 �a is the slope to the right of the vertex (…-a is the slope to the left of the vertex)

To graph y = a |x - h| + k 1. Plot the vertex (h, k) 2. Set what’s in the absolute value symbols to 0 and solving for x, gives you the x-coordinate of the vertex. The y-coordinate is k. 3. Use the slope to plot another point to the RIGHT of the vertex. 4. Use symmetry to plot a 3 rd point 5. Complete the graph

Graph y = -|x + 2| + 3 V = (-2, 3) Apply the slope a=-1 to that point 3. Use the line of symmetry x=-2 to plot the 3 rd point. 4. Complete the graph 1. 2.

Graph y = -|x - 1| + 1

Write the equation for:

v The vertex is at (0, -3) v The equation needs to be in the form y=a|x–h|+k v Therefore, y = a | x – 0 | - 3 v Find the slope to the right of the vertex to find ‘a’. v The equation is: y = 2 | x – 0 | - 3 So the equation is: y = 2|x| -3

Write the equation for: y = ½|x| + 3

Assignment Absolute Value Worksheet 1