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Algebra 1
Unit 4
GRAPHING STORIES:
Watch the videos on the next two slides
and graph the story.
GRAPHING STORIES:
Watch the video and graph the story.
Clock:
www.graphingstories.com/2kj
GRAPHING STORIES:
Watch the video and graph the story.
Height of waist off ground:
www.graphingstories.com/4my
How would you use your calculator
to solve 52?
Input
Press:
5
Output
x2
25
The number you entered is the input
number (or x-value on a graph).
The result is the output number (or yvalue on a graph).
The x2 key illustrates the idea of a
function.
A function is a relation that gives a single
output number for every valid input number.
A relation is a rule that produces one or more
output numbers for every valid input number.
There are many ways to represent relations:
Graph
Equation
Table of values
A set of ordered pairs
Mapping
These are all ways of
showing a relationship
between two variables.
A function is a rule that gives a single output number
for every valid input number.
To help remember & understand the definition:
Think of your input number, usually your
x-coordinate, as a letter.
Think of your output number, usually your
y-coordinate, as a mailbox.
A function is a rule that gives a single output number
for every valid input number.
Input number
Output number
Can you have one letter going to two different mail boxes?
Not a FUNCTION
A function is a rule that gives a single output number
for every valid input number.
Input number
Output number
Can you have two different letters going to one mail box?
Are these relations or functions?
x
1
2
3
4
y
5
6
7
Function
&
Relation
x
1
2
3
4
y
5
6
7
6
Are these relations or functions?
x
1
y
5
6
2
7
Not a Function but a
Relation
x
1
2
1
1
y
5
6
7
6
Are these relations or functions?
x
y
1
5
2
6
3
8
11
Not a function
But a relation
x
1
2
2
3
y
5
6
11
8
In words:
Double the number and add 3
As an equation:
y = 2x + 3
As a table of values:
x y
-2 -1
-1 1
0 3
1 5
These all
represent the
SAME function!
As a set of ordered pairs:
(-2, -1) (-1,1) (0,3) (1, 5) (2, 7) (3, 9)
X Y
1 5
3 4
2 3
5 4
6 5
We know it is a function because non of the “x” values in the table
repeat. We can also hold a vertical line up to the points and see
that no 2 points are touched by the same vertical line
This method of determining a function from a graph is know as the
vertical line test
#1
Is this a function?
X
Y
-2
-6
-1
-5
0
-4
1
-3
2
-2
Run vertical line across the graph and see if it touches two
places at the same time
This is a function because it passes the vertical line test.
#2
X Y
1
5
3
4
2
3
1
4
4
5
Notice the two points that are touched by the green line. This means
that the relation is not a function
Functional Notation
An equation that is a function may
be expressed using functional
notation.
The notation f(x) (read “f of (x)”)
represents the variable y.
Functional Notation Con’t
1. For the function f(x) = 2x + 6, the notation f(3) means
that the variable x is replaced with the value of 3.
f(x) = 2x + 6
f(3) = 2(3) + 6
f(3) = 12
(3, 12)
2. Evaluating Functions
Given f(x) = 4x + 8, find each:
f(2) = 4(2) + 8
= 16
(2, 16)
Evaluating More Functions
If f(x) = 3x  1, and g(x) = 5x + 3, find each:
1.
f(x) + g(x) = [3x - 1] + [5x + 3]
= 3x – 1 + 5x + 3
= 8x + 2
2.
f(x) - g(x) = [3x - 1] - [5x + 3]
= 3x – 1 – 5x - 3
= -2x - 4