1. ACT Test Prep I-2
3x³ ·2x²y ·4x²y is equivalent to: F. 9x⁷y² G. 9x¹²y² H. 24x⁷y² J. 24x¹²y K. 24x¹²y²

2. 1.2 Composition of Functions

3. Operations with Functions
Sum:
Difference:
Product:
Quotient:

4. Example 1: Given f(x) = 2x – 1 and g(x) = x², find each function.
(f + g) (x)
(f - g) (x)
(f · g) (x) d.

5. More examples:
Given f(x) = 3x² + 4x – 5 and g(x) = 2x + 9, find each function.
(f + g) (x)
(f - g) (x)
(f · g) (x) d.

6. The cost c(x) for making and selling the coffee is c(x) = 0.2x + 110.
For the Lotsa Coffee Shop, the revenue r(x) in dollars from selling x cups of coffee is r(x)=1.5 x.
The cost c(x) for making and selling the coffee is c(x) = 0.2x
Write the profit function
Profit function = revenue – cost: p(x) = r(x) – c(x)
Find the profit on 100, 200, and 500 cups of coffee sold.

7. Composition of Functions
The term "composition of functions" (or "composite function") refers to the combining of functions in a manner where the output from one function becomes the input for the next function. In math terms, the range (the y-value answers) of one function becomes the domain (the x-values) of the next function

8. The notation used for composition is: (f ◦g) (x) = f (g(x)) and is read "f composed with g of x" or "f of g of x". Notice how the letters stay in the same order in each expression for the composition. f (g(x)) clearly tells you to start with function g (innermost parentheses are done first).

9. Examples Find (f ◦ g)(x) and (g ◦ f)(x) for each f(x) and g(x).
f(x) = 2x + 5
g(x) = 3 + x
f(x) = 2x – 3
g(x)= x² - 2x
3. f(x) = x² - 2x
g(x)= 3x

10. Domains of a Composition
The domain of a composed function (f ◦ g)(x) is determined by the domains of f(x) and g(x). For example: State the domain of (f ◦ g)(x) for f(x) = g(x) =

11. State the domain of (f ◦ g)(x) for:
f(x) = g(x) = x + 3
f(x) = g(x) = 7 - x

12. Assignment
Pages – 24 even 39 Write the functions of each problem and show all work.