Identifying Functions

Front

What is a function in mathematics?

Back

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

Front

When is y considered a function of x?

Back

y is a function of x when every x value has only one corresponding y value.

Front

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

Back

A relation is not a function if at least one x value is paired with more than one y value.

Front

In the ordered pairs {(0,2), (1,3), (3,4), (4,6), (5,7), (6,8)}, is y a function of x?

Back

Yes, because every x value has only one y partner.

Front

What is the vertical line test?

Back

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

Front

If a table shows x values 1, 2, 3, 4 and corresponding y values 5, 6, 7, 8, is this a function?

Back

Yes, because every x value has only one y partner.

Front

What happens if an x value has multiple y values in a function?

Back

If an x value has multiple 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 x value gives a unique y value.

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 paired with two different y values.