2.4 – Operations with Functions

2. 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

3. I. Operations With Functions • For all functions f and g: • Sum (f + g)(x) = f(x) + g(x) • Difference (f – g)(x) = f(x) – g(x) • Product (f · g)(x) = f(x) · g(x) • Quotient ( )(x) = , where g(x) ≠ 0

4. Example

5. Solve the following:

6. Example State any domain restrictions.

7. Example 4

8. 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.

9. Example

10. Example 2

11. Example 4

12. Example 5 • A local computer store is offering a $40.00 rebate along with a 20% discount. Let x represent the original price of an item in the store. • a. Write the function D that represents the sale price after a 20% discount and the function R that represents the sale price after the $40 rebate. • b. Find the composition functions (R ° D)(x) and (D ° R)(x), and explain what they represent. • Since the 20% discount on the original price is the same as paying 80% of the original price, D(x) = 0.8x The rebate function is R(x) = x - 40 • 20% discount first $40 rebate first • R(D(x)) = R(0.8x) D(R(x)) = D(x – 40) • = (0.8x) – 40 = 0.8(x – 40) • = 0.8x – 40 = 0.8x – 32 • Notice that taking the 20% discount first results in a lower sales price.

13. Writing Activities • 5. What is the difference between (fg)(x) and (f ◦ g)(x)? Include examples to illustrate your discussion. • 6. In general, are (f ◦ g)(x) and (g ◦ f)(x) equivalent functions? Explain.

15. Homework Integrated Algebra II- Section 2.4 Level A Honors Algebra II- Section 2.4 Level B

16. End Section 2.4