Master Determining if a Mapping is a Function or Not

The video tutorial explains how to determine if a mapping is a function. It defines a function as a relation where each input uniquely maps to one output. The tutorial provides examples of valid and invalid mappings, emphasizing that inputs must not map to multiple outputs for a mapping to be considered a function.

What is a key characteristic of a function in terms of input and output mapping?

• Each input must map to a unique output.

• Inputs and outputs can be mixed freely.

• Each input can map to multiple outputs.

• Outputs can map to multiple inputs.

In a function, is it acceptable for different inputs to map to the same output?

• No, each input must have a different output.

• No, inputs and outputs must be one-to-one.

• Yes, as long as each input is uniquely mapped.

• Yes, but only if the inputs are the same.

Why is the mapping where input 8 goes to both -1 and 1 not considered a function?

• Because -1 and 1 are not valid outputs.

• Because 8 is not a valid input.

• Because 8 should map to zero.

• Because 8 maps to multiple outputs.

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

• The relation becomes a one-to-one function.

• The relation is undefined.

• The relation is not a function.

• The relation is still a function.

Which of the following is true for a relation to be a function?

• Outputs can map to multiple inputs.

• Inputs and outputs can be mixed.

• Each input must map to a unique output.

• Each output must map to a unique input.