2. How do I perform operations with function?

3. 4.2 Perform Function Operations and Compositions Example 1 Add and subtract functions Solution

4. 4.2 Perform Function Operations and Compositions Example 1 Add and subtract functions Solution c.The functions f and g each have the same domain: _____________. So the domains of f + g and f – g also consist of ________________. real numbers all real numbers

5. 4.2 Perform Function Operations and CompositionsCheckpoint. Perform the indicated operation. State the domain. all real numbers

6. 4.2 Perform Function Operations and Compositions Example 2 Multiply and divide functions Solution

7. 4.2 Perform Function Operations and Compositions Example 2 Multiply and divide functions Solution c.The domain of f consists of ________________, and the domain of g consists of ________________. So, the domain of f. g consists of ________________. all real numbers Because g(0) = _____, the domain of is restricted to ______________________. 0 all nonzero real numbers

8. 4.2 Perform Function Operations and CompositionsCheckpoint. Perform the indicated operation. State the domain. all real numbers all nonzero real numbers

9. 4.2 Perform Function Operations and Compositions Example 3 Find composition of functions Solution

10. 4.2 Perform Function Operations and Compositions Example 3 Find composition of functions Solution d.The domain of f(g(x)) consists of ________________, except x = ______ because is not in the ___________. (Not that f(0) = ____, which is __________.) The domains of g(f(x)) and f(f(x)) consist of _______________ except x = ____, again because ___________________________. all real numbers domain of f 6/0 undefined all real numbers 0 is not in the domain of f

11. 4.2 Perform Function Operations and Compositions Checkpoint. Complete the following exercises. Domain: all real numbers Domain: all real numbers Domain: all real numbers

12. 4.2 Perform Function Operations and Compositions Example 4 Solve a multi-step problem You purchase a computer with a price of $700. The computer store applies a store flyer coupon of $100 and a 12% promotional discount. Use composition to find the final price of the purchase when the coupon is applied before the discount. Use composition to find the final price of the purchase when the discount is applied before the coupon. Step 1 Write functions for the discounts. Let x be the original price, f(x) be the price after the $100 coupon, and g(x) be the price after the 12% promotional discount. Function for the $100 coupon: Function for the 12% discount:

13. 4.2 Perform Function Operations and Compositions Example 4 Solve a multi-step problem You purchase a computer with a price of $700. The computer store applies a store flyer coupon of $100 and a 12% promotional discount. Use composition to find the final price of the purchase when the coupon is applied before the discount. Use composition to find the final price of the purchase when the discount is applied before the coupon. Step 2 Compose the functions. $100 coupon is applied first: 12% discount is applied first:

14. 4.2 Perform Function Operations and Compositions Example 4 Solve a multi-step problem You purchase a computer with a price of $700. The computer store applies a store flyer coupon of $100 and a 12% promotional discount. Use composition to find the final price of the purchase when the coupon is applied before the discount. Use composition to find the final price of the purchase when the discount is applied before the coupon. Step 3 Evaluate the functions g(f(x)) and f(g(x)) when x = 700. The final price is _____ when the $100 coupon is applied before the 12% discount. The final price is _____ when the 12% discount is applied before the $100 coupon.

15. 4.2 Perform Function Operations and Compositions Checkpoint. Complete the following exercises. 6.Rework Example 4 for an original price of $800, a $110 coupon, and a 15% discount. $110 coupon is applied first: 15% discount is applied first:

16. 4.2 Perform Function Operations and Compositions Pg. 123, 4.2 #1-31