Vertical Line Test

Front

What is the Vertical Line Test?

Back

A method used 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 graph to be a function?

Back

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

Front

What is an example of a function?

Back

The graph of y = x^2 is a function because each x-value has one corresponding y-value.

Front

What is an example of a graph that is NOT a function?

Back

The graph of a circle, such as x^2 + y^2 = r^2, is not a function because a vertical line can intersect it at two points.

Front

How can you tell if a graph is a function using the Vertical Line Test?

Back

If any vertical line drawn on the graph intersects it at more than one point, then the graph is not a function.

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

Can a function have multiple outputs for a single input?

Back

No, a function cannot have multiple outputs for a single input; this would violate the definition of a function.

Front

What is a linear function?

Back

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

Front

What is a non-linear function?

Back

A function that does not graph to a straight line, such as quadratic functions, exponential functions, etc.