This document discusses absolute value functions and their graphs. It defines the parent graph of an absolute value function as f(x)=x and describes its V-shape and axis of symmetry. Examples are given of absolute value functions after various transformations from the parent graph, along with the general form y=a(x-h)+k. The document also describes how to identify the vertex and axis of symmetry from the equation of an absolute value function and how to write the equation of an absolute value function given its graph. Homework problems are assigned from the textbook.

1. 2.7 ABSOLUTE VALUE
FUNCTIONS AND GRAPHS

2. ABSOLUTE VALUE FUNCTION
 The simplest form (parent graph) of an absolute
value function is f ( x ) = x

3. ABSOLUTE VALUE FUNCTION
 The graph of f ( x ) = x 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

4. EXAMPLE
Make a table of values, then graph the function. Describe
the transformation from the parent function.
y = x −4

5. EXAMPLE
Make a table of values, then graph the function. Describe
the transformation from the parent function.
f ( x) = x + 2 + 3

6. EXAMPLE
Graph the equation. Describe the transformation from the
parent function.
1
y= x
2

7. EXAMPLE
Graph the equation. Describe the transformation from the
parent function.

8. TRANSFORMATIONS OF THE
ABSOLUTE VALUE FUNCTION

9. GENERAL FORM OF THE
ABSOLUTE VALUE FUNCTION
When translations, stretches and
compressions are combined for Absolute
Value Functions, we derive the general form:
y =a x−h +k
The stretch or compression factor is |a|, the
vertex is located at (h, k), and the axis of
symmetry is the line x = h

10. EXAMPLE
Without graphing, what are the vertex and axis of
symmetry of the graph of:
y =3 x−2 +4

11. EXAMPLE
Without graphing, what are the vertex and axis of
symmetry of the graph of:
y = −2 x − 1 − 3

12. EXAMPLE
Without graphing, what are the vertex and axis of
symmetry of the graph of:

13. WRITING AN ABSOLUTE
VALUE FUNCTION FROM A
GRAPH
1. Identify the vertex
2. Identify a, by finding the slope of the branch
on the right
3. Write the equation

14. EXAMPLE
What is the equation of the absolute value
function?

15. EXAMPLE
What is the equation of the absolute value
function?

16. WITHOUT USING A TABLE OF
VALUES GRAPH THE FUNCTION

17. HOMEWORK
 Page 111
 #9 – 21 odd
 #23 – 30 all