2.7 ABSOLUTE VALUE FUNCTIONS AND GRAPHS

ABSOLUTE VALUE FUNCTION

The simplest form (parent graph) of an absolute value function is f x x

ABSOLUTE VALUE FUNCTION

The graph of is V-shaped and symmetric about a vertical line called the axis of symmetry. The graph also has a single maxima point or minima

point, called a vertex

f x x

TRANSFORMATIONS OF THE ABSOLUTE VALUE FUNCTION

EXAMPLEMake a table of values, then graph the function. Describe the transformation from the parent function.

4y x

EXAMPLEMake a table of values, then graph the function. Describe the transformation from the parent function. 2 3f x x

EXAMPLEGraph the equation. Describe the transformation from the parent function.

1

2y x

EXAMPLEGraph the equation. Describe the transformation from the parent function.

2y x

GENERAL FORM OF THE ABSOLUTE VALUE FUNCTION

When translations, stretches and compressions are combined for Absolute Value Functions, we derive the general form:

The stretch or compression factor is |a|, the vertex is located at (h, k), and the axis of symmetry is the line x = h

y a x h k

EXAMPLEWithout graphing, what are the vertex and axis of symmetry of the graph of:

3 2 4y x

EXAMPLEWithout graphing, what are the vertex and axis of symmetry of the graph of:

2 1 3y x

WRITING AN ABSOLUTE VALUE FUNCTION FROM A GRAPH

1. Identify the vertex2. Identify a, by finding the slope of the

branch on the right 3. Write the equation

EXAMPLEWhat is the equation of the absolute value function?

EXAMPLEWhat is the equation of the absolute value function?