Identifying Functions from a function map

Front

What is a function in mathematical terms?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

How can you determine if a relation is a function?

Back

A relation is a function if every input (x-value) has exactly one output (y-value). This can be checked using the vertical line test on a graph.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a curve is a function. If a vertical line intersects the curve at more than one point, then the curve is not a function.

Front

What does it mean for a relation to not be a function?

Back

A relation is not a function if at least one input is associated with more than one output.

Front

Can a function have the same output for different inputs?

Back

Yes, a function can have the same output for different inputs, as long as each input corresponds to only one output.

Front

What is a one-to-one function?

Back

A one-to-one function is a function where each output is associated with exactly one input, meaning no two different inputs produce the same output.

Front

What is a many-to-one function?

Back

A many-to-one function is a function where multiple inputs can produce the same output.

Front

What is a one-to-many relation?

Back

A one-to-many relation is not a function because a single input is associated with multiple outputs.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.