4.6 Absolute Value FunctionsGoal p Evaluate, graph, and use simple absolute value

functions.

VOCABULARY

Vertex The common endpoint of the two rays in the graph of an absolute value function

Evaluate the function when x 5 24 and x 5 7.

a. f(x) 5 x 1 3 b. g(x) 5 x 2 5Solutiona. When x 5 24:

f(x) 5 x 1 3 Write function. f(24) 5 24 1 3 Substitute 24 for x. 5 21 Simplify. 5 1

When x 5 7:

f(x) 5 x 1 3 Write function. f(7) 5 7 1 3 Substitute 7 for x. 5 10 Simplify. 5 10 b. When x 5 24:

g(x) 5 x 2 5 g(24) 5 24 2 5 5 4 2 5

5 21

When x 5 7:

g(x) 5 x 2 5 g(7) 5 7 2 5 5 7 2 5

5 2

Example 1 Evaluate Absolute Value Functions

Your Notes

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Your Notes

Copyright McDougal Littell/Houghton Mifflin Company Lesson 4.6 Algebra 2 C&S Notetaking Guide 85

Graph y 5 1 } 3 x.

Solution

1. Plot the vertex at the origin .

2. Find a second point by substituting an x-value .

y 5 1 } 3 x Write original equation. 5 1 } 3 3 Substitute 3 for x. 5 1 } 3 ( 3 ) Evaluate 3 . 5 1 Multiply.

A second point is ( 3 , 1 ).

3. Plot the second point and use symmetry to plot a third point at ( 23 , 1 ).

4. Connect these three points with a V -shaped graph.

Example 2 Graph an Absolute Value Function

O

y

x1

1

Checkpoint Evaluate the function when x 5 22 and when x 5 5.

1. f(x) 5 x 2 7 2. g(x) 5 x 1 10

9; 2 12; 15

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Your Notes

3. y 5 4x

O

y

x1

1

4. y 5 2 1 } 4 x

O

y

x1

1

Checkpoint Graph the function.

Homework

Copyright McDougal Littell/Houghton Mifflin Company Lesson 4.6 Algebra 2 C&S Notetaking Guide 86

Graph y 5 23x.Solution

1. Plot the vertex at the origin.

2. Find a second point by substituting an x-value.

y 5 23x Write original equation.

5 23 1 Substitute 1 for x. 5 23( 1 ) Evaluate 1 . 5 23 Multiply.

A second point is ( 1 , 23 ).

3. Plot the second point and use symmetry to plot a third point at ( 21 , 23 ).

4. Connect these three points with a V-shaped graph.

Example 3 Graph an Absolute Value Function

O

y

x1

1

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