Warm up
1. -3 + 17=
4. 3x +2x -1
2. -7 – 11=
2
5. 7𝑥 − 5𝑥 − 𝑥 + 𝑥
3. 28 + -15 =
6. 10𝑦 − 2𝑦 + 5𝑥 − 2
2
Unit 2 Day 1:
Introduction to
Functions
Essential Questions: What is a function and how
do we represent its data set? What is function
notation and how do we use it?
Vocabulary
Function: a rule that establishes a relationship
between two quantities, the input (x) and the
output (y). For each input, there is exactly one
output.
• Vertical Line Test: a test that determines
whether or not a graphed equation is a function.
• Domain: the collection of all the input values.
• Range: the collection of all the output values.
•
About Functions
Explanation of a Function
•
A function is a relationship between numbers or data.
•
For each input, there is exactly one output. HOWEVER, more than
one input can have the same output.
Example of How a Function Works
•
Input: people going to parties
•
Output: parties to go to
•
So, for each person going to a party (input), there is exactly one
party to go to (output). But more than one person (input) can go to
the same party (output).
Example 1
Do the following relationships represent a function?
a)
b)
c)
input
output
input
output
input
output
0
3
0
3
0
7
1
1
1
1
1
8
3
2
3
2
2
9
4
5
4
3
10
Function
Function
Not a Function
Input-Output Tables
One way to describe a function is to make an input-output table. Lets look
at the diagram of the function f(x) = x + 3:
As a diagram:
input
As a table:
output
0
3
1
4
3
6
4
7
input
0
1
3
4
output
3
4
6
7
The collection of all input values is the domain of the function and all
the output values are the range. In the examples above, the domain is
0, 1, 3, and 4 and the range is 3, 4, 6, and 7.
Example 2: Does the table represent a function? If it
is a function, state the domain and range.
input
1
2
3
4
Day of Wk
1
2
3
4
output
3
4
5
6
Meetings
3
3
4
4
Yes;
Yes;
Domain: 1, 2, 3, 4
Domain: 1, 2, 3, 4
Range : 3, 4, 5, 6
Range: 3, 4
Month
1
1
2
3
input
1
2
1
3
# of
Holidays
2
4
1
1
output
4
4
5
5
NO
NO
The Vertical Line Test
•
•
•
The way that we can tell if a graphed equation is a
function is by using the Vertical Line Test.
If a vertical line crosses the graph only once, the graph is a function.
If the vertical line crosses more than once, it is NOT a function.
Example 3: Decide whether the graph represents y as a
function of x.
5
-5
5
5
Yes
-5
5
-5
-5
5
5
-5
5
-5
Yes
-5
5
-5
No
No
Summary
Essential Questions: What is a function and how do we
represent its data set? What is function notation and how
do we use it?
Take 1 minute to write 2 sentences answering the
essential questions.