This document discusses functions and relations. It defines a relation as a mapping of inputs to outputs, and specifies that a relation is a function only if each input maps to exactly one output. It then provides examples of relations represented as ordered pairs, tables, graphs, and equations, and asks the reader to determine whether each example represents a function or not.

2. • A relation is a mapping, or
pairing, of input values with
output values.
 “Mapping Diagram”

3. • If any input maps to more than
one output, then it is not a
function.
• Is this a function? Why or why
not?

4. YES!
NO!

5. Tell if each represents a function:
x y

6. Relations and functions can also
be represented using:
a set of ordered pairs
a table
a graph
an equation

7. Is the relation a function?
Remember: each input (x) can
only have one unique output (y)
{(0, 2), (1, 2), (3, 1), (4, 5)}
{(-2, 4), (0, 3), (-2, 2), (-4, 1)}
YES!
NO!

8. Determine whether the relation
is a function:
{(2, 6), (3, 7), (4, 8), (3, 9)}
{(1, -3), (0, -4), (-1, -3), (-2, -2)}

9. Is the relation a function?
input -2 -1 0 0 1 2
output 3 4 5 6 7 8

10. Is the relation a function?
input output
2 5
4 3
6 3

11. • A graph is a
function if no
vertical line
crosses the
graph at more
than one point.

12. Determine whether each graph
represents a function.
YES! YES! NO!

13. Determine whether each graph
represents a function.