1. 2-1: Functions & Their Graphs
Objectives:
• I will determine if a relation is a function.
• I will determine domain and range of a
relation from a graph, from a table, or from
an equation with and without restrictions.

2. Relations & Functions
Relation: a set of ordered pairs
Domain: the set of x-coordinates
Range: the set of y-coordinates
When writing the domain and range, do not
repeat values.

3. Relations and Functions
Given the relation:
{(2, -6), (1, 4), (2, 4), (0,0), (1, -6), (3, 0)}
State the domain:
D: {0,1, 2, 3}
State the range:
R: {-6, 0, 4}

4. Relations and Functions
• Relations can be written in several
ways: ordered pairs, table, graph, or
mapping.
• We have already seen relations
represented as ordered pairs.

5. Table
{(3, 4), (7, 2), (0, -1), x y
(-2, 2), (-5, 0), (3, 3)} 3 4
7 2
0 -1
-2 2
-5 0
3 3

6. Mapping
• Create two ovals with the domain on
the left and the range on the right.
• Elements are not repeated.
• Connect elements of the domain with
the corresponding elements in the
range by drawing an arrow.

7. Mapping
{(2, -6), (1, 4), (2, 4), (0, 0), (1, -6), (3, 0)}
2
-6
1
4
0
0
3

8. Functions
• A function is a relation in which the
members of the domain (x-values)
DO NOT repeat.
• So, for every x-value there is only
one y-value that corresponds to it.
• y-values can be repeated.

9. Functions
• Discrete functions consist of points
that are not connected.
• Continuous functions can be
graphed with a line or smooth
curve and contain an infinite
number of points.

10. Do the ordered pairs represent a
function?
{(3, 4), (7, 2), (0, -1), (-2, 2), (-5, 0), (3, 3)}
No, 3 is repeated in the domain.
{(4, 1), (5, 2), (8, 2), (9, 8)}
Yes, no x-coordinate is repeated.