1. Warm-Up Let f x =2𝑥 −5 and g x = 𝑥 2 −𝑥−2 Find f(x) + g(x)
Find g(x) – f(x)
Find f(x)· g(x)
Find g(x) ÷ f(x)
Find (g + f)(2)
Can also be written as…
(f+g)(x)
(g – f)(x)
(fg)(x)
( 𝑓 𝑔 ) 𝑥

2. Warm-Up Solutions Let f x =2𝑥 −5 and g x = 𝑥 2 −𝑥−2
f(x) + g(x) = 𝑥 2 +𝑥−7
g(x) – f(x) = 𝑥 2 −3𝑥+3
f(x)· g(x) = 2𝑥 3 − 7𝑥 2 +𝑥+10
g(x) ÷ f(x) = 𝑥 2 −𝑥−2 2𝑥 −5 where x≠ 5 2
(g + f)(2) = -1

3. Let f x =3𝑥+2, g x = 2𝑥 2 −2 and h x =−4𝑥 −1
Function Composition
Let f x =3𝑥+2, g x = 2𝑥 2 −2 and h x =−4𝑥 −1
g(f(x)) aka (g ◦ f)(x)
f(h(x))
h(g(2))
(g ◦ h)(-1)

4. You Try! Let 𝑓 𝑥 = 𝑥 2 𝑎𝑛𝑑 𝑔 𝑥 =2𝑥−1 Find g(f(2)) Find f(g(2))
Find g(f(x))
Find f(g(x))
Answers 7 9
2𝑥 2 −1
4𝑥 2 −4𝑥+1

5. Word Problem 1
Hannah’s Housekeeping charges a $20 flat fee plus $12 an hour to clean a house.
Write a function c(h) for the cost to clean a house for h hours.
What are the units of the domain and range of this function?
Hannah’s Housekeeping can clean one room every half hour.
Write a function h(r) for the hours needed to clean r rooms.
Write a function c(h(r)) to represent the cost of cleaning r rooms.
What is the value and meaning of c(h(12))?

6. Word Problem 2
Jim has a lawn service called Green’s Grass Guaranteed. On every mowing job, Jim charges a fixed $30 fee to cover equipment and travel expenses plus a $20 per hour labor charge.
Write a cost function where c(t) is Jim’s charge for t hours of work.
What are the unit of the domain and range in this function?
It takes Jim 4 hours to mow 1 acre. Jim prepares a cost estimate for each customer based on the number of acres of their property.
3) Write the equation of a function in terms of a for the number of hours t it will take Jim to mow the property.
4) What are the units for the domain and range of this function?
5) Write a function c(t(a)) for the cost of mowing a acres.
6) What are the units for domain and range of this function?
7) What is the value of c(t(4)) and what does it mean?

7. Word Problem 3 The average cost of gas in Illinois right now is $2.89.
1) Write a function c(g) for the cost to purchase g gallons.
A Nissan Altima gets 27 MPG.
2) Write a function g(m) for the gallons needed for a Nissan Altima to travel m miles.
Write a function c(g(m)). What does it represent? What are the units of the domain and range of this function?

8. Homework
P. 87 – 88 #2-8 evens
#10
#12-17
#24-28 evens
#29-36