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 identify a function from a set of ordered pairs?

Back

A set of ordered pairs is a function if no x-value is repeated with different y-values.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a graph represents 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), (2, 3), (1, 4)} a function?

Back

No, because the x-value 1 has two different y-values (2 and 4).

Front

Is the relation {(3, 5), (4, 6), (5, 7)} 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 + 2, where each input x gives a unique output.

Front

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

Back

An example is {(1, 2), (1, 3)}, where the x-value 1 has 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 has a unique y-value and each y-value corresponds to only one x-value.