Perform Function Operations and Composition

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!