Algebra 1

1
Algebra 1

• Introduction to Functions

2
Objective

• Students will identify functions and make an
  input/output table for a function
• An input/output table is the EXACT SAME THING as
  an xy-table

3
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

4
Identifying Functions

• The key to identifying functions is the rule that
  each input has exactly one output.
• If an input has more than one outputthen the
  data is not a function
• Often times you will be given a table or a list
  of ordered pairs be asked to identify if the data
  is a function.
• Lets look at some examples

5
Identifying Functions

• Look at the table to the rightnotice that each
  input has exactly one output
• Therefore, this set of data is considered a
  function

Input Output
5 3
6 4
7 5
8 6
6
Identifying Functions

• Look at the table to the rightnotice 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
7
Identifying Functions

• Look at the table to the rightnotice 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 outputits ok
  to have different inputs with the same output

Input Output
1 3
2 3
3 4
4 4
8
Creating Input/Output Tables

• You can create an input/output table by
  substituting given values into the rule and
  putting the results in a table
• Lets look at an example
• Suppose you are asked to create an input/output
  table for the equation y 3x 2 using the
  values of 0, 1, 2, and 3.
• Simply substitute the values of 0, 1, 2 and 3
  into the equation for x and then figure out what
  y is equal to.

9
Comments

• To get the desired results (input/output table)
  it really important that you are organized here
• We will use the methodology that we have
  previously learned about evaluating equations to
  determine the output.
• That is
• Write the equation
• Substitute
• Simplify
• Lets continue with our example

10
Example
Input Output




1. y 3x 2
3. y 3x 2
y 3(0) 2
y 3(2) 2
0
y 0 2
y 6 2
2
y 2
y 8
1
5
2. y 3x 2
4. y 3x 2
y 3(1) 2
y 3(3) 2
2
8
y 3 2
y 9 2
y 5
y 11
3
11
11
Your Turn Identifying a Function

• Does the table represent a function? Explain

3.
1.
Input Output
1 1
2 3
3 6
4 10
Input Output
1 3
2 6
3 11
4 18
2.
4.
Input Output
1 3
1 4
2 5
3 6
Input Output
5 9
4 8
3 9
2 7
12
Homework

• Students will correctly write an equation in
  function form.
• Complete worksheet --- solving for y
• 5.1 B worksheet