Vertical Line Test

Front

What is the Vertical Line Test?

Back

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

What does it mean for a relation to be a function?

Back

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

Front

How can you tell if a graph is not a function using the Vertical Line Test?

Back

If a vertical line drawn through the graph intersects it at more than one point, the graph does not represent a function.

Front

What is the domain of a function?

Back

The set of all possible x-values (inputs) for which the function is defined.

Front

What is the range of a function?

Back

The set of all possible y-values (outputs) that a function can produce.

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 corresponding y-value.

Front

What is an example of a function?

Back

The equation y = 2x + 3 is a function because for every x-value, there is exactly one y-value.

Front

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

Back

The equation x^2 + y^2 = 1 is not a function because a vertical line can intersect it at two points.

Front

What is a one-to-one function?

Back

A function where each x-value corresponds to a unique y-value, and each y-value corresponds to a unique x-value.

Front

What is a many-to-one function?

Back

A function where multiple x-values can correspond to the same y-value.