Vertical Line Test

Front

What is the Vertical Line Test?

Back

A method to determine if a graph represents a function. If any 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 crosses the graph at more than one point, the graph does not represent a function.

Front

What is an example of a function?

Back

The equation y = 2x + 3 is a function because for every x-value, there is one corresponding 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 for some x-values, there are two corresponding y-values.

Front

What is the significance of the Horizontal Line Test?

Back

The Horizontal Line Test determines if a function is one-to-one, meaning each output is produced by only one input.

Front

Can a vertical line ever be a function?

Back

No, a vertical line represents a relation where every x-value corresponds to multiple y-values, thus failing the Vertical Line Test.

Front

What is the domain of a function?

Back

The set of all possible input values (x-values) for the function.

Front

What is the range of a function?

Back

The set of all possible output values (y-values) for the function.

Front

What does it mean if a function is linear?

Back

A linear function is a function that graphs to a straight line, represented by the equation y = mx + b.