4.8 Functions and Relations A relation is any set of ordered pairs. A function is a special kind of relation. It is a set of ordered pairs that has exactly one output for each input. The students are the inputs, their test scores are the outputs. It wouldn’t make sense to have more than one test score for a single student. FUNCTION!! The x values are the inputs, the y values are the outputs. There are more than one y values for each x value. RELATION!! Function or relation?? Sometimes it helps to list the input/output table as a list of ordered pairs to determine if it is a function or a relation. Vertical Line Test: No vertical line can intersect the graph of a function at more than one place. If the vertical line intersects the graph at more than one place, then the graph is a relation, not a function. Function Notation: To evaluate a function when it is in function notation… plug in the value of x everywhere you see x in the equation. Examples: 1. Evaluate f (x) = 8x − 1 when x = 3 2. Evaluate f (x) = −5x − 1
3. Evaluate f (x) = 2(x + 5) − 1
when x = −4 when x = 6