1. Section 6.5 Operations with Functions
Algebra 2
Section 6.5
Operations with Functions

2. Warm Up
Simplify. Assume that all expressions are defined. #1 2𝑥+5 −( 𝑥 2 +3𝑥−2) #2 (𝑥−1) 𝑥+1 2 #3 𝑥 2 −𝑥−6 𝑥 2 −4

3. Operations on functions is very much like operations on expressions.
You’re creating a new function!

4. Addition 𝒇+𝒈 𝒙=𝒇 𝒙 +𝒈(𝒙) Example 𝑓 𝑥 =2 𝑥 2 −5𝑥+11 𝑔 𝑥 =5 𝑥 2 +2𝑥−30
𝑓+𝑔 𝑥=2 𝑥 2 −5𝑥+11+5 𝑥 2 +2𝑥−30
𝑓+𝑔 𝑥=7 𝑥 2 −3𝑥−19
Would 𝑔+𝑓 𝑥 be a different function?

5. Subtraction 𝒇−𝒈 𝒙=𝒇 𝒙 −𝒈(𝒙) 𝑓 𝑥 =4𝑥−2 𝑔 𝑥 =6𝑥+8 𝑓−𝑔 𝑥= 4𝑥−2 − 6𝑥+8
𝑓−𝑔 𝑥=4𝑥−2−6𝑥−8
𝑓−𝑔 𝑥=−2𝑥−10
Would 𝑔−𝑓 𝑥 be a different function?

6. Try these
Pg #2-4

7. Multiplication 𝒇𝒈 𝒙=𝒇(𝒙)∙𝒈(𝒙) 𝑓 𝑥 =𝑥−3 𝑔 𝑥 =4𝑥+2 𝑓𝑔 𝑥= 𝑥−3 4𝑥+2
𝑓𝑔 𝑥= 𝑥−3 4𝑥+2
𝑓𝑔 𝑥= 4𝑥 2 +2𝑥−12𝑥−6
𝑓𝑔 𝑥=4 𝑥 2 −10𝑥−6
Would 𝑔𝑓 𝑥 be a different function?

8. Division 𝒇 𝒈 x= 𝒇(𝒙) 𝒈(𝒙) 𝒈(𝒙)≠𝟎 𝑓 𝑥 = 𝑥 2 +7𝑥+12 𝑔 𝑥 =𝑥+3
𝑓 𝑔 𝑥= 𝑥 2 +7𝑥+12 𝑥+3
𝑓 𝑔 𝑥= (𝑥+4)(𝑥+3) (𝑥+3)
𝑓 𝑔 𝑥=𝑥+4

9. Same or Different?
Would 𝑓 𝑔 𝑥 and 𝑔 𝑓 𝑥 be the same function?

10. Try these!
Pg. 446 #5-7

11. Composition of functions
Composition of functions- this operation uses the output of one function as the input of another function
𝒇𝒐𝒈 𝒙=𝒇 𝒈 𝒙
This operation is NOT commutative!!!
𝒈𝒐𝒇 𝒙=𝒈(𝒇 𝒙 )

13. Start with the innermost parentheses 1st!

14. Try These!
Pg. 8-10

15. Boots are 50% off Take an additional 40% off Are you getting 90% off
Boots are 50% off Take an additional 40% off Are you getting 90% off? When you get 40% off, what percent of the price are you paying?

16. 𝑔 𝑥 =.50𝑥
𝑓 𝑥 =.40𝑥
𝑓𝑜𝑔 𝑥=𝑓 𝑔 𝑥
𝑓 .50𝑥 = 𝑥
What percent are you getting off of the original price?

17. 𝑓 𝑥 = 2𝑥 2 𝑔 𝑥 =𝑥+2 Find 𝑓𝑜𝑔 𝑥= ? 𝑔𝑜𝑓 𝑥= ?

18. Try these!
Pg #11-14

19. Homework/Classwork
Pg #15-33 all, all