Introduction to functions: functions vrs relations, domain, and range.

1. Functions
2222 holes by flickr user jared

2. What is a function? Let's play a game ...
All functions are relations, but not all relations are functions.

3. Relations x 2+ y 2= 25
one-to-many
Functions
one-to-one many-to-one
y=x-2 y = x2

4. Relations x 2+ y 2= 25
one-to-many
Functions
one-to-one many-to-one
y=x-2 y = x2

5. Domain & Range of a Function
Symbolically
y=x-2
1 -2
mapping
4 5
9 -2 Graphically
output
input
range
domain
Numerically
{(1, -2), (4, 5), (9, -2)}

6. R
D
Functions or Relations?
write as ordered pairs
2
2 -1
-1
-3
-4 5
3
R
R D
D
6
-1
2
2
-4
8
-3 -4
R
D
D R

7. Domain & Range of a Function
Domain:
Range:

8. Functions or Relations? relation
function
Identify the domain and range of each.
relation
DOMAIN
(3, 2), (2, 3), (3, 3)
RANGE
function
(1, 4), (4, 1), (-1, 4)
DOMAIN
RANGE
relation
(-5, 2), (0, 2), (-5, 3) DOMAIN
RANGE
function
(5, -2), (3, 2), (6, 2) DOMAIN
RANGE

9. Example 1
An example of a relation, that is a function is:
x y
-2 -4 y=x-2
-1 -3
0 -2
1 -1
2 0
An example of a relation, that is NOT a function is:
xy
-3 -4
x 2 + y 2= 25
-3 4
0 -5
05
43
What's The Verticle Line Test?

10. The Verticle Line Test
Sweep a vertical line across the
graph of the function. If the line
crosses the graph more than
y = x2 once it is not a function, only a
relation.

11. HOMEWORK
Exercise #48 & #49