1. 2-1 Relations & Functions
M11.D.1.1.2: Determine if a relation is a function given a set of points or a graph
M11.D.1.1.3: Identify the domain, range, or inverse relation

2. Objectives
Graphing Relations Identifying Functions

3. Vocabulary
A relation is a set of pairs of input and output values. You can write a relation as a set of ordered pairs. ex. {(2,1), (-3,0), (4,10), (9, -4)}
Input
Output

4. Graphing a Relation
Graph the relation {(–3, 3), (2, 2), (–2, –2), (0, 4), (1, –2)}.
Graph and label each ordered pair.

5. Vocabulary
The domain of a relation is the set of all inputs, or x-coordinates of the ordered pairs.
The range of a relation is the set of all outputs, or y-coordinates of the ordered pairs.

6. Finding Domain & Range
Write the ordered pairs for the relation. Find the domain and range.
{(–4, 4), (–3, –2), (–2, 4), (2, –4), (3, 2)}
The domain is {–4, –3, –2, 2, 3}.
The range is {–4, –2, 2, 4}.

7. Vocabulary
A mapping diagram links elements of the domain with the corresponding elements of the range.
Ex. A mapping diagram for the relation {(-1, -2), (3,6), (-5, -10), (3,2)}
-10 -2 2 6 -5 -1 3

8. Making a Mapping Diagram
Make a mapping diagram for the relation {(–1, 7), (1, 3), (1, 7), (–1, 3)}.
Pair the domain elements with the range elements.

9. Vocabulary
A function is a relation in which each element of the domain is paired with exactly one element of the range.

10. Identifying Functions
Determine whether the relation is a function.
The element –3 of the domain is paired with both
4 and 5 of the range.
The relation is not a function.
{(-3,4), (-3,5), (2,5)}
If its written as ordered pairs, look for x values that duplicate.

11. Using the Vertical-Line Test
Use the vertical-line test to determine whether the graph represents a function. If a vertical line passes through at least two points on the graph, then the graph is not a function.
If you move an edge of a ruler from left to right across the graph, keeping the edge vertical as
you do so, you see that the edge of the ruler never intersects the graph in more than one point in any position.
Therefore, the graph does represent a function.

12. Vocabulary You read the function notation f(x) as “f of x”.
NOTE: this does not mean “f times x”
When the value of x is 3, f(3), represents the value of the function at x = 3

13. Function Notation Find ƒ(2) for each function. a. ƒ(x) = –x2 + 1
ƒ(2) = – = –4 + 1 = –3
b. ƒ(x) = |3x|
ƒ(2) = |3 • 2| = |6| = 6
c. ƒ(x) = 9
1 – x
ƒ(2) = = = –9 9
1 – 2 –1

14. Homework
Pg 59 # 1,2,5,6,8,9,12,13,16,17,22