2.7 Absolute Value Functions and Graphs

1
2.7 Absolute Value Functions and Graphs

• Graphing Absolute Value Functions

2
Absolute Value Functions

• An absolute value function is a function with an
  absolute value as part of the equation
• f(x) mx b
• Graphs of absolute value equations have two
  special properties
• a) a vertex
• b) they look like angles

3
Absolute Value Functions















Vertex point where the graph changes direction

4
Finding the Vertex

• For an equation y mx b c,
• vertex -b , c
• m
• Example Find the vertex of y 4x 2 - 3
• Answer -2 , -3
• 4
• -1 , -3
• 2

5
Absolute Value Functions

• Steps to graphing an absolute value function
• Find the vertex
• Write two linear equations and find slope
• Use slope to plot points, connect the dots

6
Absolute Value Functions

• Example 1
• Graph y 3x 12.

7
Absolute Value Functions

• Step 1 Find the vertex
• y 3x 12
• m 3 -b -12 c 0
• vertex -b , c
• m
• vertex -12 , 0
• 3
• vertex (-4, 0)

8
Absolute Value Functions

• Step 1 Find the vertex
• vertex (-4, 0)

9
Absolute Value Functions

• Step 2 Write two linear equations and find
  slope.
• y 3x 12
• Positive Negative
• y 3x 12 y -3x 12
• m1 3 m2 -3

10
Absolute Value Functions

• Step 3 Use the slope to plot points
• vertex (-4, 0)
• m1 3
• m2 -3

11
Absolute Value Functions

• Try at your desk
• Graph y x
• Graph y 4x 7
• Graph y 3x 2
• Graph y 42x 1 5

12
Absolute Value Functions

• Try at your desk
• Graph y x
• Graph y 4x 7
• Graph y 3x 2
• Graph y 42x 1 5