Unit 3: Functions and Transformations
3.1 Functions and Relations
Relation: when a set of points follow a rule such as
a set of ordered pairs
Function: a relation where every x value has a single y value
Domain: the set of all x values in a relation
Range: the set of all y values in a relation
Just like the y values are dependent on the x values, the range is dependent on the domain
Ex 1 Determine if the following relations are functions; state the domain and the range
(a) a parabola opening to the left
(b) a line
(c) a graph looking like the number 7
(d) {(1,3), (2,4), (4,9), (3,7), (2,6)}
(e)
|
x |
y |
|
2 |
4 |
|
1 |
2 |
|
0 |
1 |
|
-1 |
2 |
|
-2 |
5 |
(f)
|
x |
y |
|
7 |
6 |
|
5 |
3 |
|
5 |
4 |
|
3 |
1 |
|
1 |
0 |
A relation can be shown to be a function if the graph of the relation passes a vertical line test.
There are a couple of ways of naming functions also. There are one-to-one functions and one-to-many functions.
One-to-one function: a function where every y value has a single x value
One-to-many function: a function that is not one-to-one
A function is one-to-one if it passes a horizontal line test.
p. 178#1-3,5,11,13,15,17,18,21