Download Chapter 2 - Graphing Linear Relations and

4-1: Relations and Functions
Objectives:
• Understand, draw, and determine if a
relation is a function.
• Graph & write linear equations,
determine domain and range.
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:
State the range:
R:
Relations and Functions
• Relations can be written in several
ways: ordered pairs, tables, graphs, 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)}
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.
Do the ordered pairs represent a
function?
Ex. 1
{(3, 4), (7, 2), (0, -1), (-2, 2), (-5, 0), (3, 3)}
Ex. 2
{(4, 1), (5, 2), (8, 2), (9, 8)}
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 or No
D:
R:
x
Yes or No
D:
R:
y
y
Does the graph represent a function?
Name the domain and range.
x
Yes or No
D:
R:
x
Yes or No
D:
R:
y
y
Does the graph represent a function?
Name the domain and range.
x
Yes or No
D:
R:
x
Yes or No
D:
R:
y
y
Function Notation
• When we know that a relation is a
function, the “y” in the equation can
be replaced with f(x).
• f(x) is simply a notation to designate a
function. It is pronounced ‘f’ of ‘x’.
• The ‘f’ names the function, the ‘x’ tells
the variable that is being used.
Value of a Function
Since the equation y = x - 2
represents a function, we can also
write it as f(x) = x - 2.
Find f(4):
Value of a Function
If g(s) = 2s + 3, find g(-2).
Value of a Function
If h(x) = 4x2 – 3x + 1, find h(-2)
Find the Domain & Range when
given the Equation
1.) f(x) = 1/4x – 5
2.) f(x) = (x – 3)2
3.) f(x) = |x| - 4
4.) f(x) = -x2 + 3