Identifying Functions

Front

What is a function?

Back

A function is a relation where each input (x-value) has exactly one output (y-value).

Front

How can you determine if a graph represents a function?

Back

A graph represents a function if any vertical line drawn through the graph intersects it at most once.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a graph is a function by checking if a vertical line crosses the graph more than once.

Front

What does it mean if an x-value has two corresponding y-values in a relation?

Back

If an x-value has two corresponding y-values, the relation is not a function.

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 has 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.

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 has two different y-values.

Front

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

Back

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

Front

What is a mapping diagram?

Back

A mapping diagram visually represents a function by showing how each input is paired with its 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 the function.