Absolute value functions have a V-shaped graph. There are three main ways to graph an absolute value function: using a table of values, using a graphing calculator, or interpreting the equation. The vertex of an absolute value graph is always the x-coordinate inside the absolute value signs. To graph, one finds the vertex and then plots additional points on either side, connecting them to form the V-shape. The number outside the absolute value signs moves the graph up or down, while the number inside moves it left or right.

1. Absolute Value Functions & Graphs Parent function of Abs. Functions y = |x|

2. Absolute Value Functions Spin on linear equations V-shaped graph Has a feel of graphing a linear function. All Absolute Value graphs are in the same form: Where b and c will be real numbers.

3. Graphing Absolute Value Functions Three ways to graph: Use a table Use a TI “ Read” the equation. If you can read a linear eqn., you can read an absolute value eqn.

4. Using a Table The table method works for every two-variable equation in the world. Choose an x-value Sub in the value for x Simplify Your answer is the y-value and now you’ve found a point on the graph. Repeat for 2-4 more x-values and sketch the function. There’s just one problem…

5. The Vertex Abs. Value graphs have two directions. Plot vertex first!! The vertex for ALL Abs. Value functions is at:

6. Example 1 Graph 1. Identify b and c b= 1 c= -2 2. Find the vertex x= y = -2 3. Choose two x-values greater than the x coord. of the vertex and two less than. Lets choose -4,-2, 1, 2. x |x+1| -2 y -4 |-4 + 1| - 2 1 -2 |-2 + 1| - 2 -1 1 | 1 + 1| - 2 0 2 | 2 + 1| - 2 1 4. Set up a table

7. Using the TI: Get your Calc! Make sure the function is solved for y. Hit the ‘y=‘ button Clear out any “old” functions Hit ‘math’ -> move over to ‘num’ -> hit enter Abs( says “take the absolute value of the expression in the parenthesis. Enter the expression and close the parenthesis. If there’s a ‘c’, put it in Hit graph and there it is! Hopefully…if not, hit ‘zoom’ and choose zoomfit or zoomstd

8. Example 2 Go to into ‘y=‘ ‘ math’ -> move over to ‘num’ -> hit enter Enter the expression ‘x-3’ Close parenthesis!!!!! Then put in +2 Hit Graph Zoom, if needed Graph:

9. “ Read the Equation” The ‘c’ on the outside of the bars moves the parent function up/down. Positive is up, negative is down. The ‘b’, the constant on the inside of the abs. value bars moves the parent function left/right the OPPOSITE of what you see. Positive goes left and negative goes right. To flip the V upside-down, there must be a negative number multiplied on the outside of the bars.

10. Example 3 Graph: Place Parent Function Move left or right– here we’ll go left to -5 Move up or down– here we’ll go down to -2 Done 