Identifying Functions

Front

What is a function?

Back

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

Front

How can you determine if a graph represents a function?

Back

A graph represents a function if no vertical line intersects the graph at more than one point.

Front

What does it mean for an x-value to repeat in a relation?

Back

If an x-value repeats, it means that there are multiple y-values associated with that x-value, which means the relation is not a function.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a graph is a function by checking if any vertical line crosses the graph more than once.

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 has only one corresponding y-value.

Front

What is an example of a function?

Back

An example of a function is f(x) = x^2, where each x-value has one unique y-value.

Front

What is an example of a non-function?

Back

An example of a non-function is the relation {(1, 2), (1, 3)}, where the x-value 1 has two different y-values.

Front

What is a one-to-one function?

Back

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

Front

What is a many-to-one function?

Back

A many-to-one function is a function where multiple x-values can map to the same y-value.

Front

What is a relation?

Back

A relation is a set of ordered pairs, which may or may not be a function.