The document contains information about functions, including: 1) Two tables that represent different functions - y as a function of x, and distance as a function of time. 2) Examples of evaluating functions f(x) at different values of x. 3) Definitions and examples of addition, subtraction, multiplication, and division of functions. 4) Examples of combining two functions using addition, subtraction, and multiplication.

1. Functions

2. y 2 8 50 98
x 0 1 4 6
Table of values that represents y as a
function of x.
2 2
y = 2x + 4x + 2 f(x) = 2x + 4x + 2
A function is a relation in which each
x­ value has exactly one y­ value

4. distance 90 270 360 540 720
time 1 3 4 6 8
Table of values that shows distance as a
function of time.
d = 90t d(t) = 90t

5. 2
Given f(x) = x + 3x ­ 4
evaluate f(1) f(3) f(7)

6. Given: f(x) = 1 g(x) = 2x + 3
x ­ 1
Addition: Same as:
(f + g)(x) = f(x) + g(x)

7. Given: f(x) = 1 g(x) = 2x + 3
x ­ 1
Subtraction: Same as:
(f ­ g)(x) f(x) ­ g(x)

8. Given: f(x) = 1 g(x) = 2x + 3
x ­ 1
Multiplication: Same as:
.
(f g)(x)
.
f(x) g(x)

9. Given: f(x) = 1 g(x) = 2x + 3
x ­ 1
Division: Same as:
. f(x)
.
(f g)(x) where g(x) = 0
g(x)

10. Given:
2
f(x) = x ­ 5x + 2 g(x) = ­3x + 4
Find (f + g)(x)

11. 2
f(x) = x ­ 5x + 2 g(x) = ­3x + 4
Find (f ­ g)(x)

12. 2
f(x) = x ­ 5x + 2 g(x) = ­3x + 4
.
Find (f g)(x)

13. 2
f(x) = x ­ 5x + 2 g(x) = ­3x + 4
Find f(g(x))
2
f(x) = (­3x + 4) ­ 5(­3x + 4) + 2