24 – Operations with Functions by hcj

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									    2.4 – Operations with Functions
• Objectives:
  – Perform operations with functions to
    write new functions
  – Find the composition of two functions

• Standard:
  – 2.8.11.S. Analyze properties and
    relationships of functions
Warm Up:
Example 1
Example 1a
Example 2
Example 2a
     Composition of Functions
      • Let f and g be functions of x.

• The composition of f and g, denoted f ◦ g,
           is defined by f(g(x)).

  • The domain of y = f(g(x)) is the set of
  domain values of g whose range values
   are the domain of f. The function f ◦ g is
  called the composite function of f with g.
Example 3
Example 3a
                          2
           Let f(x) = -2x + 3 and g(x) = -2x.
   a. Find f ◦ g.                        b. Find g ◦ f.



                      2                                   2
  a. f(g(x)) = -2 (-2x) + 3             b. g(f(x)) = -2 (-2x +3)
            = -8x2 + 3                             = 4x2- 6
Example 4
Lesson Quiz
   Homework
    Practice 2.4

Ch 2 Test: Tue 10/27

								
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