3.4 Absolute Value Functions

Absolute Value is defined by:

0 xif x,-0 x if 0,0 xif x,

x

The graph of this piecewise function consists of 2 rays, is V-shaped and opens up.

To the left ofx=0 the line isy = -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| + kVertex is at (h,k) & is symmetrical in the line

x=hV-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| > 1a 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| + k1. 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 3rd point5. Complete the graph

Graph y = -|x + 2| + 31. V = (-2,3)2. Apply the

slope a=-1 to that point

3. Use the line of symmetry x=-2 to plot the 3rd point.

4. Complete the graph

Graph y = -|x - 1| + 1

Write the equation for:

So the equation is:y = 2|x| -3

The vertex is at (0, -3)

The equation needs to be in the form

y = a | x – h | + k

Therefore, y = a | x – 0 | - 3

Find the slope to the right of the vertex to find ‘a’.

The equation is: y = 2 | x – 0 | - 3

Write the equation for:

y = ½|x| + 3

Assignment - Absolute Value Worksheet 1