Function or Not?

Front

What is the vertical line test?

Back

The vertical line test is a method used to determine if a graph represents a function. If any vertical line intersects the graph at more than one point, the graph does not represent a function.

Front

What defines a function in mathematics?

Back

A function is a relation that assigns exactly one output (y-value) for each input (x-value).

Front

What does it mean for a relation to be 'not a function'?

Back

A relation is 'not a function' if at least one input (x-value) is associated with more than one output (y-value).

Front

How can you tell if a set of ordered pairs represents a function?

Back

A set of ordered pairs represents a function if no x-value is repeated with different y-values.

Front

What is an example of a function?

Back

An example of a function is the set of ordered pairs {(1, 2), (2, 3), (3, 4)} because each x-value is unique.

Front

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

Back

An example of a relation that is not a function is the set of ordered pairs {(1, 2), (1, 3), (2, 4)} because the x-value '1' is associated with two different y-values.

Front

What is the significance of repeating x-values in a function?

Back

Repeating x-values in a function can indicate that the relation is not a function if they correspond to different y-values.

Front

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

Back

If a graph fails the vertical line test, it means that there are at least two points on the graph that share the same x-coordinate, indicating that it is not a function.

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 corresponds to only one y-value.

Front

What is a one-to-one function?

Back

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