Function vs Not a Function

Front

What is a function in mathematics?

Back

A function is a relation between a set of inputs (x-values) and a set of possible outputs (y-values) 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 x-value has exactly one corresponding y-value.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a curve is a function. If any vertical line intersects the curve at more than one point, 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 x-value is associated with more than one y-value.

Front

Can a function have the same y-value for different x-values?

Back

Yes, a function can have the same y-value for different x-values, as long as each x-value corresponds to only one y-value.

Front

What is an example of a function?

Back

An example of a function is f(x) = x^2, where each input x has a unique output x^2.

Front

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

Back

An example of a relation that is not a function is {(1, 2), (1, 3)}, where the x-value 1 is associated with two different y-values.

Front

What is a one-to-one function?

Back

A one-to-one function is a function where each x-value corresponds to a unique y-value and each y-value corresponds to a unique x-value.

Front

What is a many-to-one function?

Back

A many-to-one function is a function where multiple x-values can correspond to the same y-value.

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.