1. Identifying Functions

2. A sequence of inputs and outputs paired together
A Relation
A sequence of inputs and outputs paired together

3. Input and output grouped in parentheses The input is listed first
Ordered Pairs
Input and output grouped in parentheses
The input is listed first
The output is second
( Venus, 19), (Mars, 5), (Earth, 7), etc.
If inputs and outputs are both numbers, we get the same ordered pairs we are used to using for graphs
(1, 7), (2, 4), (3, 6), …

4. A relation, where each input has only one output.
A Function
A relation, where each input has only one output.
Note: if inputs do not repeat, the relation is automatically a function. If inputs do repeat, then each repetition must match to the same output.
(2, 7), (3, 4), (4, 7) is a function.
(2, 7), (3, 4), (3, 7) is not a function since the input 3 maps to two outputs 4 and 7.

5. A Function Not a Function
Vertical Line Test
A vertical line passed over a function, will only cross the function at one point at a time.
A Function Not a Function

6. Domain and Range of a Relation
Domain is a list of allowed inputs
Note this graph has inputs of x ≥ 1
In interval notation, this is [1, ∞ )
The bracket is “squared” since 1 is included
Range is the resulting outputs
The range is all real numbers
In interval notation ( –∞, ∞)