Determining Functions: Key Concepts and Techniques

The video tutorial explains how to determine if a mapping is a representation of a function. It introduces the concept of functions as relations where each input uniquely maps to one output. The tutorial provides examples of mappings that qualify as functions and those that do not, emphasizing the importance of unique input-output relationships. It clarifies that different inputs can map to the same output, but a single input cannot map to multiple outputs.

What is a function in terms of input and output?

• A relation where inputs and outputs are the same

• A relation where each input uniquely maps to one output

• A relation where each input maps to multiple outputs

• A relation where outputs are not related to inputs

In a function, what must be true about the inputs?

• Each input can map to multiple outputs

• Each input must map to a unique output

• Inputs do not need to map to any output

• Inputs can map to the same output

If an input maps to different outputs, what can be concluded?

• It is a special type of function

• It depends on the outputs

• It is not a function

• It is still a function

Can different inputs map to the same output in a function?

• Yes, but only if the inputs are the same

• No, each input must map to a different output

• Yes, as long as each input uniquely maps to that output

• No, it is not allowed in any case

What is an example of a valid function mapping?

• 8 maps to 11, 9 maps to 3

• 11 maps to 8, 11 maps to 9

• 7 maps to -2, 7 maps to 3

• 1 maps to 4, 1 maps to 5

Why is the mapping '8 goes to -1 and 8 goes to 1' not a function?

• Because -1 is not a valid output

• Because 8 maps to multiple outputs

• Because 8 is not a valid input

• Because 1 is not a valid output

What happens if an input maps to more than one output?

• It is not considered a function

• It becomes a different type of function

• It is still considered a function

• It is invalid in any context

In the example where '1 goes to 3 and 1 goes to 4', why is it not a function?

• Because 1 maps to multiple outputs

• Because 3 is not a valid output

• Because 1 is not a valid input

• Because 4 is not a valid output

What is the key characteristic of a function?

• Inputs and outputs are the same

• Outputs are not related to inputs

• Each input maps to multiple outputs

• Each input maps to a unique output

Why is the mapping '2 goes to 5 and 2 goes to 6' not a function?

• Because 2 maps to multiple outputs

• Because 5 is not a valid output

• Because 2 is not a valid input

• Because 6 is not a valid output