Identifying Functions

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

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), …

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.

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

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 ( –∞, ∞)