Relations and Functions

Front

What is a function in mathematics?

Back

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

Front

What is the definition of a relation?

Back

A relation is a set of ordered pairs, where each pair consists of an input and an output.

Front

What is the domain of a function?

Back

The domain is the set of all possible input values (x-values) for a function.

Front

What is the range of a function?

Back

The range is the set of all possible output values (y-values) for a function.

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

Can a function have repeating x-values?

Back

Yes, a function can have repeating x-values as long as each x-value corresponds to only one y-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 x-value is paired with more than one y-value.

Front

How can you determine if a mapping is a function?

Back

To determine if a mapping is a function, check if each input (x-value) has exactly one output (y-value).

Front

What is an example of a function?

Back

An example of a function is f(x) = 2x + 3, 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)}, where the x-value 1 is paired with two different y-values.