Graphing Absolute Equations & Inequalities

Graphing on the Calculator   1. Enter the formula for the function you wish to graph using the Y= editor. 2. Set the

viewing window. WINDOW 3. Graph the function. GRAPH 4. Adjust the viewing window, if necessary.   Example. Graph the absolute value function. This function is “built-in” and we can use

it by entering its name.   Step 1. Press [Y=] to display the Y= editor. Press [2ND] [0 (CATALOG)]

and select “abs(“ from the menu. Next, press [ ] and [ )].  

Step 2. We assume the Standard window has been selected. The standard window is rectangular, which distorts the graph. ZOOM:4 will make a square window.   Step 3. Press [GRAPH] to obtain the graph of the absolute value function.

Graphing using tablesLook at this site for absolute value functions

graphed using a table of values.

http://www.purplemath.com/modules/graphabs.htm

The Absolute Value “Parent Graph”The “parent graph” of an absolute value function is . (See the graph at right) The vertex of the graph is the turning point and is at the origin (0, 0). The left and right sides of the graph have slopes = .

xy

1x

y

-5

-4

-3

-2

-1

1

2

3

4

5

vertex (0, 0)

y= -x (when x<0, slope= -1) y=x (when x>0, slope=1)

Transformations of the Graphs of the Absolute Value Function

The transformed graphs of an absolute value function have the equation , where the vertex of the graph is (h, k) and the slopes = . Graph each set of functions and state how the graphs change.

khxaxf )(

a

Examples1. Graph: What happens to the graph of as

h increases? 2. Graph: What happens to the graph of as

h decreases? 3. Graph: What happens to the graph of as

k increases?

4. Graph: What happens to the graph of as k decreases?

 5. Graph: What happens to the graph of as

a increases (approaching infinity)? 6. Graph: What happens to the graph of as

a decreases, approaching zero?

1 xy

1 xy

5 xy

7 xy

xy2

1

xy 5

khxaxf )(Makes the graph wider,more narrow, or flips

Makes the graph moveleft or right, oppositethe sign

Makes the graph moveUp or down, same as sign

Absolute Value InequalitiesClick on this link to do inequalities

http://www.mathwarehouse.com/algebra/linear_equation/absolute-value-functions-inequality.html