1. Functions
MATHPOWERTM 11, WESTERN EDITION
5.5.1

2. A function is a relation in which no two ordered pairs have
Functions
A function is a relation in which no two ordered pairs have
the same first coordinate. For every x there is only one y.
(1, 2) (2, 4) (3, 6) (4, 8)
A relation that is a FUNCTION
(1, 2) (2, 4) (2, 5) (3, 6)
A RELATION that is not a function 1 2 3 2 3 4 1 2 3 2 3 4 1 2 3 2 3 4
FUNCTION
FUNCTION
RELATION
5.5.2

3. Vertical Line Test: If no two points on a graph can
Functions
Vertical Line Test: If no two points on a graph can
be joined by a vertical line, the
graph is a function.
Function
Relation
Function
5.5.3

4. An equation that is a function may be expressed
Functional Notation
An equation that is a function may be expressed
using functional notation. The notation f(x)
(read “f at (x)”) represents the variable y.
E.g., y = 2x + 6 can be written as f(x) = 2x + 6.
Given the equation y = 2x + 6, evaluate when x = 3.
y = 2(3) + 6
y = 12
For the function f(x) = 2x + 6, the notation f(3) means
that the variable x is replaced with the value of 3.
f(x) = 2x + 6
f(3) = 2(3) + 6
f(3) = 12
5.5.4

5. Given f(x) = 4x + 8, find each:
Evaluating a Function
Given f(x) = 4x + 8, find each:
1. f(2)
2. f(a)
f(a) = 4(a) + 8
= 4a + 8
f(2) = 4(2) + 8
= 16
3. f(a + 1)
4. f(-4a)
f(a + 1) = 4(a + 1) + 8
= 4a
= 4a + 12
f(-4a) = 4(-4a) + 8
= -16a+ 8
5.5.5

6. If f(x) = 3x - 1 and g(x) = 5x + 3, find each:
Evaluating a Function
If f(x) = 3x - 1 and g(x) = 5x + 3, find each:
f(2) + g(3)
2. f(4) - g(-2)
= [3(2) -1] + [5(3) + 3] =
= 23
= [3(4) - 1] - [5(-2) + 3]
= (-7)
= 18
f(1) + 2g(2)
= 3[3(1) - 1] + 2[5(2) + 3] =
= 32
5.5.6

7. If g(x) = 2x2 + x - 3, find each:
Evaluating a Function
If g(x) = 2x2 + x - 3, find each:
1. g(2)
g(2) = 2(2) =
= 7
2. g(x + 1)
g(x + 1) = 2(x + 1)2 + (x + 1) - 3
= 2(x2 + 2x + 1) + x
= 2x2 + 4x x - 2
= 2x2 + 5x
5.5.7