1. 6.3 Function Operations and Composition SWBAT perform operations with functions

2. Review function operations of +, -, x,
If 𝑓 𝑥 =5 𝑥 and 𝑔 𝑥 =−11 𝑥 1 3
find: a) 𝑓 𝑥 +𝑔(𝑥)
b) 𝑓 𝑥 −𝑔(𝑥)
c) domain of 𝑓+𝑔
d) domain of 𝑓−𝑔
5 𝑥 −11 𝑥 =−6 𝑥 1 3
16 𝑥 1 3
All reals
All Reals

3. If 𝑓 𝑥 =8𝑥 and 𝑔 𝑥 =2 𝑥 5 6
find: a) 𝑓(𝑥)∙𝑔(𝑥)
b) 𝑓(𝑥) 𝑔(𝑥)
c) domain of 𝑓∙𝑔
d) domain of 𝑓 𝑔
16 𝑥 11 6
4 𝑥 1 6
All reals ≥0
All reals >0

4. **power function**
𝑦=𝑎 𝑥 𝑏 is a power function if b is a rational number.
ie. 𝑦=6 𝑥 2 3

5. 𝐶 𝑥 =2500+75𝑥 when x is the number of printers sold. Find 𝑅 𝑥 −𝐶 𝑥 .
A small company sells computer printers over the Internet. The company’s total monthly revenue R and costs C are modeled by the functions 𝑅 𝑥 =120𝑥 and,
𝐶 𝑥 = 𝑥 when x is the number of printers sold.
Find 𝑅 𝑥 −𝐶 𝑥 .
Explain what this ‘difference’ means.
− 𝑥 𝑜𝑟
45𝑥−2500
𝑅 𝑥 −𝐶 𝑥 = Profit

6. Find f(g(3)) Find 𝑔(𝑓 3 ) Find f(g(x)) Find g(f(x))
** Composition of functions** another function operation, putting functions ‘inside’ other functions. (The inner most part first.) If 𝑓 𝑥 =𝑥+2 and 𝑔 𝑥 = 𝑥 2
Find f(g(3))
𝑔 3 =9, 𝑡ℎ𝑒𝑛𝑓 9 =11, 𝑠𝑜 𝑓 𝑔 3 =11
Find 𝑔(𝑓 3 )
𝑓 3 =5, 𝑡ℎ𝑒𝑛 𝑔 5 =25, 𝑠𝑜 𝑔 𝑓 3 =25
Find f(g(x))
𝑓 𝑥 2 = 𝑥 2 +2
Find g(f(x))
𝑔 𝑥+2 = 𝑥+2 2 = 𝑥 2 +4𝑥+4

7. What is the value of 𝑓(𝑔 −3 )? Let 𝑓 𝑥 =6 𝑥 −2 and 𝑔 𝑥 =4𝑥+5
Find a) 𝑓(𝑔 𝑥 )
b) 𝑔(𝑓 𝑥 )
c) 𝑔(𝑔 𝑥 )
d) the domain of each composition
𝑓 8 =20
𝑓 4𝑥+5 =6 4𝑥+5 −2 = 6 16 𝑥 2 +40𝑥+25
𝑔 6 𝑥 −2 =4 6 𝑥 −2 +5= 24 𝑥 2 +5
𝑔 𝑔 𝑥 =4 4𝑥+5 +5=16𝑥+25
A) 𝑎𝑙𝑙 𝑟𝑒𝑎𝑙𝑠 ≠ − 𝑏) 𝐴𝑙𝑙 𝑟𝑒𝑎𝑙𝑠 ≠ 𝑐) 𝑎𝑙𝑙 𝑟𝑒𝑎𝑙𝑠

8. Your starting wage for your part time job was $6 an hour
Your starting wage for your part time job was $6 an hour. All employees get a 5% raise after 6 months. You are given an additional raise of $.75/hour as a reward for your outstanding work.
Find the new hourly wage if the 5% raise is applied before the $.75 raise/hour.
Find the new hourly wage if the $.75 raise/hour is applied before the 5% raise.
=$7.05
=$7.09

9. Questions? Day 6 Assignment