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

What is the vertical line test?

Back

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

Front

Is the relation {(1, 2), (1, 3), (2, 4)} a function?

Back

No, because the x-value 1 has two y-values (2 and 3).

Front

Is the relation {(1, 2), (2, 3), (3, 4)} a function?

Back

Yes, because each x-value has only one y-value.

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 paired 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 has only one y-value.

Front

What is an example of a function?

Back

An example of a function is f(x) = x + 1, where each input x gives 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 domain in a function?

Back

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

Front

What is the definition of a range in a function?

Back

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