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 y to be a function of x?

Back

For every x-value, there is exactly one corresponding y-value.

Front

What is the domain of a function?

Back

The set of all possible x-values that can be input into the function.

Front

What is the range of a function?

Back

The set of all possible y-values that can be output from the function.

Front

If a graph passes the Vertical Line Test, what can we conclude?

Back

The graph represents a function.

Front

If a graph does not pass the Vertical Line Test, what can we conclude?

Back

The graph does not represent a function.

Front

Example of a function: y = 2x + 3. Does it pass the Vertical Line Test?

Back

Yes, it passes because for every x, there is one y.

Front

Example of a non-function: y^2 = x. Does it pass the Vertical Line Test?

Back

No, it does not pass because a vertical line can intersect the graph 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 vice versa.

Front

What is a many-to-one function?

Back

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