1. Boise State University
Graphing Functions
James Brennan
Boise State University

2. Functions
A function associates one and only one output (y) with each input (x).
f(x) y x

3. Function Notation
Input
Name of Function
Output

4. Function Definitions
Functions can be defined by
Input-Output Table
Written Rule
Formula

5. Example: y = 2x - 1 x y –2 2(–2) – 1 = –5 –5 –1 2(–1) – 1 = –3 –3
FORMULA y –2
2(–2) – 1 = –5 –5 –1
2(–1) – 1 = –3 –3
2(0) – 1 = –1 –1 1
2(1) – 1 = 1 2
2(2) – 1 = 3 3
2(3) – 1 = 4 5

6. Graphing the (x, y) Pairs
(–2, –5)
(–1, –3)
(0, –1)
(1, 1)
(2, 3)
(3, 5)

7. After Many Points x y

8. Summary
The graph of a function is the plot of all (x, y) pairs that make the function true.
The plot of the points can be a straight line or a curve.