Is it a Function? Key Concepts and Examples

The video tutorial introduces the concept of functions, explaining that a function is a special type of relation where each input has a unique output. Using a vending machine analogy, the video illustrates how functions work. It provides examples to differentiate between functions and non-functions, using a set of inputs and outputs, a mapping diagram, and a graph. The tutorial emphasizes that for a relation to be a function, each input must map to a single, unique output.

What is a function in mathematics?

• A relation where inputs and outputs are the same

• A relation where each output has a unique input

• A relation where each input has a unique output

• A relation where inputs can have multiple outputs

In the vending machine analogy, what does pressing a1 and getting chips represent?

• An output with a unique input

• An input with multiple outputs

• An input with a unique output

• An output with multiple inputs

Why is the relation in Example 1 not considered a function?

• Because the inputs are not unique

• Because each input has a unique output

• Because the input 3 has two different outputs

• Because the outputs are not unique

In Example 1, what are the outputs for the input 3?

• 6 and -9

• -5 and 6

• 4 and -1

• -8 and 6

In Example 2, why is the relation considered a function?

• Because the inputs are not unique

• Because each output is used more than once

• Because each input has a unique output

• Because each input is used more than once

Which of the following inputs is not repeated in Example 2?

• 0

• 3

• 6

• 9

In the mapping diagram, why is the relation considered a function?

• Because each output is used more than once

• Because each input has a unique output

• Because each input is used more than once

• Because the inputs are not unique

In the mapping diagram, how many inputs map to the output 2?

• Three

• Four

• One

• Two

Why is the graph in Example 3 not considered a function?

• Because the outputs are not unique

• Because each input has a unique output

• Because each input is used only once

• Because some inputs are used more than once

In the graph, which input is used twice?

• 4

• 1

• 2

• 3