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Perform Function Operations and Composition

Perform Function Operations and Composition. Notes 3 – Section 6.3. Essential Learnings. Students will understand and be able to write an expression for the composite of two functions. Students will understand and be able to determine inverses using composite functions.

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Perform Function Operations and Composition

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  1. Perform Function Operations and Composition Notes 3 – Section 6.3

  2. Essential Learnings • Students will understand and be able to write an expression for the composite of two functions. • Students will understand and be able to determine inverses using composite functions. • Students will be able to evaluate composite functions of integer values.

  3. Vocabulary Power function – a function of the form y = axb where a is a real number and b is a rational number.

  4. Operations on Functions Let f and gbe any two functions. A new function hcan be defined by performing any of the four basic operations onf and g.

  5. Operations on Functions Addition: Subtraction: Multiplication: Division:

  6. Domain • The domain of h consists of the x-values that are in the domains for both f and g. • The domain of the quotient must exclude x-values for which g(x) = 0. • When taking an even root ( ¼ , ½ ), x-values must be nonnegative real numbers.

  7. Example 1 (3 – 9) Given:

  8. Example 1 cont. (12 – 18) Given:

  9. Example 2 (3 – 9) Given:

  10. Example 3 (12 – 18) Given:

  11. Class Problem Find the following and identify domain for each:

  12. Class Problem Solution Find the following and identify domain for each:

  13. Class Problem Solution Find the following and identify domain for each:

  14. Composition of Functions • The composition of a function g with a function f is h(x) = g(f(x)). • The domain of h is the set of all x-values such that x is in the domain of f and f(x) is in the domain of g .

  15. Example 4 (21 – 27) Given: Find the given value.

  16. Example 5 (29 – 35) Given: Perform the operation and state the domain.

  17. Example 5 cont. (29 – 35) Given: Perform the operation and state the domain.

  18. Assignment p.432: 3 – 36 (x3) Unit Study Guide 4 Remember to make up points on Accuracy Checks in ICE!

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