Introduction to Functions & Function Notation Section 3.5 Introduction to Functions & Function Notation

VOCAB Relation : a set of ordered pairs Domain: the set of input values (x-values); the independent variables. Range: the set of output values (y-values); the dependent variables. Function: a relation in which each value in the domain is assigned to exactly one value in the range.

ex: Identify the domain and range ex: Identify the domain and range. Then, state if the relation is a function. Year, x Rate per 1000 People, y 2000 14.7 2001 14.1 2002 13.9 2003 2004 14.0 2005

Looking at a graph… Use the Vertical Line Test: If a vertical line can be drawn that will intersect the graph at more than ONE point, then it is NOT a function!

Function Notation… Consider the equation y = 2x + 1. That is a function. To re-write using function notation, just replace y with f(x). So, y = 2x + 1 becomes… f(x) = 2x + 1

Evaluating functions Given a function f(x), to find f(a) just substitute a in for x and simplify. Evaluate each using f(x) = 2x – 4 f(2) f(-1) f(-½)

Graphing Functions If it is a LINEAR function: f(x) = mx + b graph using slope and y-intercept. If it is NONLINEAR, make a quick x|y table. Use -2, -1, 0, 1, and 2 for the x-values then sub in to find the y-values. Plot and connect.

EX: graph. State the domain and range. 1. f(x) = ½ x – 2 2. f(x) = x2 - 1