Functions and Their Domains

Front

What is the definition of a function?

Back

A function is a relation in which each input (x-value) is associated with exactly one output (y-value).

Front

What is the domain of a function?

Back

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

Front

What is the range of a function?

Back

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

Front

How can you determine if a relation is a function?

Back

A relation is a function if no x-value is repeated with different y-values.

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

Identify the domain of the relation {(1,2), (2,3), (3,4)}.

Back

The domain is {1, 2, 3}.

Front

Identify the range of the relation {(1,2), (2,3), (3,4)}.

Back

The range is {2, 3, 4}.

Front

Is the relation {(1,2), (1,3), (2,4)} a function?

Back

No, because the x-value 1 has two different y-values (2 and 3).

Front

What is an example of a function?

Back

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