Identifying Functions

Front

What is a function in mathematics?

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

What is the vertical line test?

Back

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

Front

What does it mean for a mapping to be a function?

Back

A mapping is a function if every input (x-value) corresponds to exactly one output (y-value).

Front

Can a function have the same output for different inputs?

Back

Yes, a function can have the same output for different inputs, but each input must map to only one output.

Front

What is an example of a relation that is not a function?

Back

A relation where an input maps to multiple outputs, such as {(1, 2), (1, 3)}, is not a function.

Front

What is the definition of a one-to-one function?

Back

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

Front

What is the definition of 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 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.

Front

How can you determine if a set of ordered pairs represents a function?

Back

You can determine if a set of ordered pairs represents a function by checking if any x-value appears more than once with different y-values.