Download Aim: What are relations and functions? How do we find domain and

Aim: What are relations and
functions? How do we find domain
and range?
Do Now:
1) Evaluate : -2(x + 1) when x = 5
2) Solve the equation: -x + 9 = 2x – 27
3) Solve for y: -x – y = 10
HW #6 – Chapter 4 pg 126 #3-11
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.
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}
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.
Table
{(3, 4), (7, 2), (0, -1),
(-2, 2), (-5, 0), (3, 3)}
x
3
7
0
-2
-5
3
y
4
2
-1
2
0
3
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.
Mapping
{(2, -6), (1, 4), (2, 4), (0, 0), (1, -6), (3, 0)}
2
1
0
3
-6
4
0
Consider the relation given by the ordered
pairs{(-2,-3),(-1,1),(1,3),(2,-2),(3,1)}
a. Identify the domain and range.
b. Represent the relation using a
table and a mapping diagram.
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 yvalue that corresponds to it.
• y-values can be repeated.
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.
Do the ordered pairs represent a function?
1){(3, 4), (7, 2), (0, -1), (-2, 2), (-5, 0), (3, 3)}
No, 3 is repeated in the domain.
2){(4, 1), (5, 2), (8, 2), (9, 8)}
Yes, no x-coordinate is repeated.
Graphs of a Function
Vertical Line Test:
If a vertical line is passed over
the graph and it intersects the
graph in exactly one point, the
graph represents a function.
Does the graph represent a function?
Name the domain and range.
x
Yes
D: all reals
R: all reals
y
x
y
Yes
D: all reals
R: y ≥ -6
Does the graph represent a function?
Name the domain and range.
x
No
D: x ≥ 1/2
R: all reals
y
x
y
No
D: all reals
R: all reals
Does the graph represent a function?
Name the domain and range.
x
Yes
D: all reals
R: y ≥ -6
y
x
y
No
D: x = 2
R: all reals