1. Functions
And Function Notation

2. Definitions
Relation
A relationship between sets of information. Typically between inputs and outputs.
Function
A relation such that there is no more than one output for each input.
(each x should have a single unique y)
(Must pass the vertical line test)

3. 4 Examples of Functions X Y 10 2 15 -5 18 20 1 7 X Y -3 1 -1 4 5 7 3

4. 3 Examples of Non-FunctionsY 4 1 10 2 11 -3 5 3

5. Functional Notation
An equation that is a function may be expressed using functional notation.
The notation f(x) (read “f of (x)”) represents the variable y.

6. Functional Notation Cont’d
Example:
y = 2x + 6 can be written as f(x) = 2x + 6.
Another example:
z = 3g + 1 can be written as f(g) = 3g+1.
Write the following in function notation:
1. w = -2r
w(r) = -2r or f(r) = -2r
2. p = 5v – 4
p(v) = 5v – or g(v) = 5v – 4

7. Functional Notation Con’t
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

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

10. Determine the value of x when given f(x).
Given f(x) = 4x + 8, determine x when:
f(x) = 2
f (x) = -1

12. Evaluating More Functions
If f(x) = 3x  1, and g(x) = 5x + 3, find each:
f(2) + g(3)
= [3(2) -1] + [5(3) + 3] =
= 23
f(4) - g(-2)
= [3(4) - 1] - [5(-2) + 3]
= (-7)
= 18
f(1) + 2g(2)
= 3[3(1) - 1] + 2[5(2) + 3] =
= 32