Algebra 1
Ch 4.8 – Functions and Relations
Do Now
1. Find the slope between these two points:
m
y 2  y1 2  (4) 6


 2
x 2  x1
3  0
3
(0,-4) and (-3,2)
2. Rewrite the equation in slope-intercept form, and
then tell me the slope
and y-intercept.

y = mx + b
6x  3y  30
y = 2x - 10
-6x
-6x
-3y = -6x + 30
m = 2/1
b = (0,-10)
3. Rewrite the equation in slope-intercept form, and

then tell me the slope and y-intercept.
5x  y  3
+5x
+5x
y = 5x - 3
m = 5/1
b = (0,-3)
Do Now Cont’d
4. Rewrite the equation in slope-intercept form, and
then graph it.
-2y = -3x - 12
3x  2y 12  0

-2
-2 -2
3
y  x 6
2
3
m=
b = (0,6)
2
-3x
-3x
-2y + 12 = -3x
-12
-12
5. Decide whether thegraphs of the two equations
NO THEY ARE NOT
are parallel lines.
y  3x  4  0
2y  6x  5

y  3x  4
PARALLEL
5 DIFFERENT SLOPES!!
y  3x 
2
Functions
A relationship where one thing depends upon
another is called a function.
 A function is a rule that establishes a
relationship between two quantities called the
input and output.
 In a function each input has exactly one
output. More than one input can have the
same output
You can’t have one input go to TWO different outputs!!!

Domain and Range
A relation is any set of ordered pairs.
The set of all first components of the order
pairs is called the domain of the function or
relation, and the set of all second components
is called the range of the function or relation.
x
y
Input
Output
Domain
Range
Ex 1: Determine whether each
relation is a function.
a. {(4,5), (6, 7), (8,8)} Yes!!!!
b. {(5, 6), (4, 7), (6, 6), (6, 7)}
NO!!!!
Because the 6 outputs a 6 and
a7
Practice Exercises
Determine whether each relation is a
function. Give the domain and range
for each relation.
1. {( 7, 7), ( 5, 5), ( 3, 3), (0, 0)}
2. {(4,1), (5,1), (4, 2)}
Answers
1. Domain {7, 5, 3, 0}
Range {7, 5, 3, 0}
Given relation is a function.
2. Domain {4,5}
Range {1, 2}
Given relation is not a function.
Function Notation
The special notation f ( x), read "f of x"
or "f at x," represents the value of the
function at the number x.
The notation f ( x) does not mean
"f times x."
x
y
Input
Output

Domain
Range
f (x)  2x  3
y  2x  3
They mean the
same thing
f (x)
Ex 3: Evaluating a Function
If f(x) = x2 – 10x – 3, evaluate each:
a. f(-1)
b. f(2)
c. f(-4)
(-1)2 – 10(-1) - 3
(2)2 – 10(2) - 3
1 + 10 – 3
4 – 20 – 3
16 + 40 – 3
8
-19
53
(-4)2 – 10(-4) - 3
Is this a function???


Look at the table to the
right…notice that each
input has exactly one
output…
Yes it is!!!
Input
Output
5
3
6
4
7
5
8
6
Is this a function??


Look at the table to the
right…notice that the
input of 9 has two
different outputs (5 and
4 respectively)
Therefore, this set of
data is not considered
to be a function
Input
Output
9
5
9
4
8
3
7
2
Is this a function???


Look at the table to the
right…notice that the input
of 1 and 2 have the same
output of 3
In this instance this is
considered a function
because each input has
exactly one output…it’s ok
to have different inputs
with the same output
Input
Output
1
3
2
3
3
4
4
4
Make a input-output table of the function y = 3x + 2,
with the values 0, 1, 2, and 3
1. y = 3x + 2
y = 3(0) + 2
3. y = 3x + 2
y = 3(2) + 2
y=0+2
y=6+2
y=2
y=8
2. y = 3x + 2
y = 3(1) + 2
4. y = 3x + 2
y = 3(3) + 2
y=3+2
y=9+2
y=5
y = 11
Input
Output
0
2
1
5
2
8
3
11
Your Turn – Identifying a Function
Does the table represent a function? Explain

3.
1.
Input
1
2
3
4
YES
Output
1
3
6
10
Input
2.
Input
Output
1
1
2
3
3
4
5
6
No
1
2
3
4
Output
3
6
11
18
YES
4.
Input
Output
5
4
3
2
9
8
9
7
YES
The Vertical Line Test
The vertical line test is used to determine if a
graph is a function.
Created by:
David W. Cummins
If a vertical line passes through a graph more
than once, the
graph is not the
graph of a
function.
Pass a pencil across
the graph held
vertically to represent
a vertical line.
The pencil crosses the graph
more than once. This is not a
function because there are two
y-values for the same x-value.
So that means if we input
the x-value of 2, it has two
different outputs.
So this is a
function!!!
So this is NOT
a function!!!
So this is a
function!!!
So this is NOT
a function!!!
So this is a
function!!!
So this is NOT
a function!!!