To understand and graph absolute value functions is to know what each of the letters in the formula do to the graph.
f(x)= a|x-h|+k

"a" determines whether the function is steep or wide and whether is opens up or opens down.
When "a" is a small # it gets steeper.
When "a" is a big # it gets wider.
*Note: Basically, this number is the slope of the function.*
When "a" is a negative # it opens down.
When "a" is a positive # it opens up.

"h" determines if the function is on the left or right side on the graph.
When "h" is positive the function moves left.
When "h" is negative the function moves right.
*Note: They move opposite on the number line.*

"k" determines if the function is higher or lower on the graph.
When "k" is positive the function moves up on the graph.
When "k" is negative the function moves down on the graph.

If you know all of that, then it will be simple to graph. A much faster way than using tables.
Example:

f(x)= 3|x+2|+5

You can see that the "k" is 5 and the "h" is 2.
So you should move the function up 5 and over 2 to the left.
That will be your vertex and 3 is your slope.

To write an equation, just do the steps backwards.



Practice Problems:

1) Graph the following function.
f(x)= -5|x-1|+4


2) Graph the following function.
f(x)= |x+3|-2


3) Write the equation for the graph shown.