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

2. 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.

3. 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

4. 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!

5. Function Notation…
Consider the equation y = 2x 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

6. 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)

7. 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.

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