Function vs Non-Function

Front

What is a function?

Back

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

Front

What is a non-function?

Back

A non-function is a relation where at least one input (x-value) has more than one output (y-value).

Front

What is the vertical line test?

Back

The vertical line test is 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 is the horizontal line test?

Back

The horizontal line test is used to determine if a function is one-to-one. If a horizontal line intersects the graph at more than one point, the function is not one-to-one.

Front

Example of a function: y = 2x + 3. Is this a function?

Back

Yes, because for every x-value, there is exactly one y-value.

Front

Example of a non-function: y^2 = x. Is this a function?

Back

No, because for some x-values, there are two corresponding y-values.

Front

What does it mean for a graph to pass the vertical line test?

Back

It means that for every x-value, there is only one y-value, confirming it is a function.

Front

What does it mean for a graph to fail the vertical line test?

Back

It means that there is at least one x-value that corresponds to multiple y-values, indicating it is not a function.

Front

If a graph is a straight line, does it always represent a function?

Back

Yes, as long as it is not vertical, it will represent a function.

Front

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

Back

A relation where a single x-value corresponds to multiple y-values, such as a circle.