Identify Functions

Front

What is a function in mathematical terms?

Back

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

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 is not a function.

Front

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

Back

A relation is not a function if at least one x-value is associated with more than one y-value.

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 an example of a function?

Back

An example of a function is the relation {(1,2), (2,3), (3,4)}, where each x-value has a unique y-value.

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 {(1,2), (1,3), (2,4)}, where the x-value 1 corresponds to two different y-values.

Front

What is the significance of the x-value in a function?

Back

The x-value (input) in a function determines the corresponding y-value (output). Each x-value must be unique in a function.

Front

How can you determine if a graph is a function?

Back

You can determine if a graph is a function by using the vertical line test; if a vertical line crosses the graph more than once, it is not a function.

Front

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

Back

A graph passes the vertical line test if every vertical line drawn intersects the graph at most once, indicating that it is a function.

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.