Unit 2: Graphing Linear Equations and
Inequalities
Introduction to Functions
Section 1.7
PG 46
Coordinate Plane Vocabulary

2 lines that intersect at a
right angle
1.
2.
3.
4.
5.
6.
7.
Origin
Quadrant 1 (+,+)
Quadrant 2 (-, +)
Quadrant 3 (-, -)
Quadrant 4 (+, -)
X axis
Y axis
Vocab

Ordered pairs – a pair of #s used to identify a point in a
plane

Relation – any set of ordered pairs (x,y)

Input/Domain – collection of all the input values or xvalues

Output/Range – collection of all the output values or yvalues
Function
 a rule that establishes a relationship between 2
quantities (an input and an output).


Each input has one (and only one) output.
More than 1 input can have the same output.
f
Example:
f(x)= x2 + 1
f(2)= 22 + 1
f(2)= 5
You can view anything in the world as a function!
Plant
Mom
Input-Output Tables

For a relationship to be a function, it must be
true that for each input, there is exactly one
output.

To make your own input-output table, substitute
the given input values into the given equation
for x, then solve for y.
Examples

Determine whether each table represents a function.
Explain.
INPUT
OUTPUT
INPUT
OUTPUT
INPUT
OUTPUT
1
7
0
-7
1
4
2
8
1
-7
2
5
3
9
2
-5
2
6
4
10
3
-4
3
7
Examples

Make an input-output table for the function. Use 0, 1, 2, 3
as the domain.
INPUT
OUTPUT
INPUT
OUTPUT
INPUT
OUTPUT
Keystone Application
CW
 Pg.
49 # 1, 2, 4-7
HW
 Pg.
49-50 #10-21, 25-26
Functions and Relations
Section 4.8
PG 256
Review




A relation is a set of ordered pairs.
The set of all inputs or x-coordinates is called the Domain.
The set of all the outputs or y-coordinates is called the
Range.
In order for a relation to be a function, every input (xvalue) must correspond with exactly one output (y-value)
Examples

Decide whether the relation shown is a function. If it is, give
the domain and range.
Input
1
2
3
4
Output
2
4
5
Input
1
2
3
4
Output
5
7
Input
4
6
8
Output
0
1
4
9
4) Is the set of ordered pairs
{(-4,1 ) (-3,2 ) ( -2,5) ( -1,1)}
a function?
Input
Output
Vertical Line Test


More Info...
Used to determine whether or not a graph represents a
function.
A graph represents a function if and only if no vertical line
passes through two or more points on the graph.
Vertical Line Test
Video
Function Notation
The symbol f(x) replaces y
 Stands for “the value of f at x”
 Can be read simply as “f of x ”
 You may also see g( x), h( x), etc. used instead
of f(x )

Examples: Evaluate the function for the given value
of the variable.
Examples:
CW

Pg 259 #1, 3-9
HW

Pg 259-260 #11-19 all 20-28 evens