6.3 Function Operations and Composition SWBAT perform operations with functions

Review function operations of +, -, x, If 𝑓 𝑥 =5 𝑥 1 3 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 1 3 −11 𝑥 1 3 =−6 𝑥 1 3 16 𝑥 1 3 All reals All Reals

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

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

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 =2500+75𝑥 when x is the number of printers sold. Find 𝑅 𝑥 −𝐶 𝑥 . Explain what this ‘difference’ means. −2500+45𝑥 𝑜𝑟 45𝑥−2500 𝑅 𝑥 −𝐶 𝑥 = Profit

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

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 ≠ −5 4 𝑏) 𝐴𝑙𝑙 𝑟𝑒𝑎𝑙𝑠 ≠0 𝑐) 𝑎𝑙𝑙 𝑟𝑒𝑎𝑙𝑠

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. 6 1.05 +.75=$7.05 6.75 1.05 =$7.09

Questions? Day 6 Assignment