\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)

Functions

What is a Function?

Calculating the Output of a Function

Exercise
  • Rule: \(\textcolor{olive}{\text{add 2}}\)
  • Input: \(\textcolor{colordef}{3}\)
  • Output:

The output is \(\textcolor{colordef}{3}\textcolor{olive}{+2} =\textcolor{colorprop}{5}\).

Exercise
  • Rule: \(\textcolor{olive}{\text{subtract 3}}\)
  • Input: \(\textcolor{colordef}{5}\)
  • Output:

The output is \(\textcolor{colordef}{5}\textcolor{olive}{-3} =\textcolor{colorprop}{2}\).

Exercise
  • Rule: \(\textcolor{olive}{\text{multiply by 2}}\)
  • Input: \(\textcolor{colordef}{3}\)
  • Output:

The output is \(\textcolor{colordef}{3}\textcolor{olive}{\times 2} =\textcolor{colorprop}{6}\).

Exercise
  • Rule: \(\textcolor{olive}{\text{divide by 2}}\)
  • Input: \(\textcolor{colordef}{8}\)
  • Output:

The output is \(\textcolor{colordef}{8}\textcolor{olive}{\div 2} =\textcolor{colorprop}{4}\).

Exercise
  • Rule: \(\textcolor{olive}{\text{add 4}}\)
  • Input: \(\textcolor{colordef}{7}\)
  • Output:

The output is \(\textcolor{colordef}{7}\textcolor{olive}{+4} =\textcolor{colorprop}{11}\).

Exercise
  • Rule: \(\textcolor{olive}{\text{subtract 5}}\)
  • Input: \(\textcolor{colordef}{10}\)
  • Output:

The output is \(\textcolor{colordef}{10}\textcolor{olive}{-5} =\textcolor{colorprop}{5}\).

Exercise
  • Rule: \(\textcolor{olive}{\text{multiply by 4}}\)
  • Input: \(\textcolor{colordef}{6}\)
  • Output:

The output is \(\textcolor{colordef}{6}\textcolor{olive}{\times 4} =\textcolor{colorprop}{24}\).

Exercise
  • Rule: \(\textcolor{olive}{\text{divide by 4}}\)
  • Input: \(\textcolor{colordef}{20}\)
  • Output:

The output is \(\textcolor{colordef}{20}\textcolor{olive}{\div 4} =\textcolor{colorprop}{5}\).

Table of Values

Finding the Rule of a Function

Exercise
For these inputs and outputs, find the rule:
Input 2 4 6
Output 5 7 9
\(\textcolor{olive}{\text{Rule}}\):

  • \(\textcolor{colordef}{2}\textcolor{olive}{+\,3} = \textcolor{colorprop}{5}\)
  • \(\textcolor{colordef}{4}\textcolor{olive}{+\,3} = \textcolor{colorprop}{7}\)
  • \(\textcolor{colordef}{6}\textcolor{olive}{+\,3} = \textcolor{colorprop}{9}\)
So, the rule is \(\textcolor{olive}{\text{add 3}}\).

Exercise
For these inputs and outputs, find the rule:
Input 5 8 11
Output 3 6 9
\(\textcolor{olive}{\text{Rule}}\):

  • \(\textcolor{colordef}{5}\textcolor{olive}{-\,2} = \textcolor{colorprop}{3}\)
  • \(\textcolor{colordef}{8}\textcolor{olive}{-\,2} = \textcolor{colorprop}{6}\)
  • \(\textcolor{colordef}{11}\textcolor{olive}{-\,2} = \textcolor{colorprop}{9}\)
So, the rule is \(\textcolor{olive}{\text{subtract 2}}\).

Exercise
For these inputs and outputs, find the rule:
Input 1 2 3
Output 2 4 6
\(\textcolor{olive}{\text{Rule}}\):

  • \(\textcolor{colordef}{1}\textcolor{olive}{\times\,2} = \textcolor{colorprop}{2}\)
  • \(\textcolor{colordef}{2}\textcolor{olive}{\times\,2} = \textcolor{colorprop}{4}\)
  • \(\textcolor{colordef}{3}\textcolor{olive}{\times\,2} = \textcolor{colorprop}{6}\)
So, the rule is \(\textcolor{olive}{\text{multiply by 2}}\).

Exercise
For these inputs and outputs, find the rule:
Input 2 6 10
Output 1 3 5
\(\textcolor{olive}{\text{Rule}}\):

  • \(\textcolor{colordef}{2}\textcolor{olive}{\div\,2} = \textcolor{colorprop}{1}\)
  • \(\textcolor{colordef}{6}\textcolor{olive}{\div\,2} = \textcolor{colorprop}{3}\)
  • \(\textcolor{colordef}{10}\textcolor{olive}{\div\,2} = \textcolor{colorprop}{5}\)
So, the rule is \(\textcolor{olive}{\text{divide by 2}}\).

Calculating the Outputs of a Function

Exercise
For the rule "add 2", , complete the table of values:
Input 2 3 4
Output

  • \(\textcolor{colordef}{2}\textcolor{olive}{+ 2} = \textcolor{colorprop}{4}\)
  • \(\textcolor{colordef}{3}\textcolor{olive}{+ 2} = \textcolor{colorprop}{5}\)
  • \(\textcolor{colordef}{4}\textcolor{olive}{+ 2} = \textcolor{colorprop}{6}\)

Exercise
For the rule "add 3", , complete the table of values:
Input 0 5 10
Output

  • \(\textcolor{colordef}{0}\textcolor{olive}{+ 3} = \textcolor{colorprop}{3}\)
  • \(\textcolor{colordef}{5}\textcolor{olive}{+ 3} = \textcolor{colorprop}{8}\)
  • \(\textcolor{colordef}{10}\textcolor{olive}{+ 3} = \textcolor{colorprop}{13}\)

Exercise
For the rule "subtract 5", , complete the table of values:
Input 6 12 20
Output

  • \(\textcolor{colordef}{6}\textcolor{olive}{- 5} = \textcolor{colorprop}{1}\)
  • \(\textcolor{colordef}{12}\textcolor{olive}{- 5} = \textcolor{colorprop}{7}\)
  • \(\textcolor{colordef}{20}\textcolor{olive}{- 5} = \textcolor{colorprop}{15}\)

Exercise
For the rule "multiply by 10", , complete the table of values:
Input 2 5 20
Output

  • \(\textcolor{colordef}{2}\textcolor{olive}{\times 10} = \textcolor{colorprop}{20}\)
  • \(\textcolor{colordef}{5}\textcolor{olive}{\times 10} = \textcolor{colorprop}{50}\)
  • \(\textcolor{colordef}{20}\textcolor{olive}{\times 10} = \textcolor{colorprop}{200}\)

Exercise
For the rule "divide by 5", , complete the table of values:
Input 5 10 20
Output

  • \(\textcolor{colordef}{5}\textcolor{olive}{\div 5} = \textcolor{colorprop}{1}\)
  • \(\textcolor{colordef}{10}\textcolor{olive}{\div 5} = \textcolor{colorprop}{2}\)
  • \(\textcolor{colordef}{20}\textcolor{olive}{\div 5} = \textcolor{colorprop}{4}\)