Transcript Chapter 2 - Graphing Linear Relations and Functions - pams

1-6 and 1- 7: 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: {0,1, 2, 3}
State the range:
R: {-6, 0, 4}
Relations and Functions
• Another way to represent a relation is
to use a mapping diagram.
• 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
Mapping
The elements of the
domain are called inputs,
and the elements of the
range are called outputs.
Relations and Functions
• Sometimes a relation is represented by
a table.
x
y
{(3, 4), (7, 2), (0, -1),
3
4
7
2
(-2, 2), (-5, 0), (3, 3)}
0
-2
-5
3
-1
2
0
3
Relations and Functions
• Another way to represent a relation is
to draw its graph.
{(3, 4), (7, 2), (0, -1),
(-2, 2), (-5, 0), (3, 3)}
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.
Functions
• When no two elements of the
domain are mapped to the same
elements of the range, it is called
one-to-one mapping.
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.
Graphs of a Function
A horizontal line is a constant function.
A linear function is a function
whose graph is a line or part of a
line.
Graphs of a Function
If a vertical line is passed over the
graph and it intersects the graph in
exactly one point, the graph
represents a function.
Is the graph a function? Why/not?
x
y
x
y
Is the graph a function? Why/not?
x
y
x
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):
f(4) = 4 - 2
f(4) = 2
Value of a Function
If g(s) = 2s + 3, find g(-2).
g(-2) = 2(-2) + 3
=-4 + 3
= -1
g(-2) = -1