Identifying Functions

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) such that each input is related to exactly one output.

Front

How can you determine if a mapping represents a function?

Back

A mapping represents a function if every x-value is paired with exactly one y-value. This can be checked using the vertical line test.

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, then the curve is not a function.

Front

What does it mean if a relation is not a function?

Back

If a relation is not a function, it means that at least one input (x-value) is associated with more than one output (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 a one-to-one function?

Back

A one-to-one function is a function where each output (y-value) is associated with exactly one input (x-value), meaning no two different x-values map to the same y-value.

Front

What is a many-to-one function?

Back

A many-to-one function is a function where multiple x-values can map to the same y-value, but each x-value still maps to only one 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.

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

What is an example of a function?

Back

An example of a function is f(x) = 2x + 3, where each input x produces a unique output.