Domain and Range

Front

What is a function?

Back

A function is a relation that assigns exactly one output value for each input 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 a vertical line intersects the graph at more than one point, the graph does not represent a function.

Front

What does it mean for a relation to be a function?

Back

A relation is a function if every input (x-value) has 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 the domain of a function from its graph?

Back

The domain can be determined by identifying the x-values that the graph covers.

Front

How can you determine the range of a function from its graph?

Back

The range can be determined by identifying the y-values that the graph covers.

Front

What is an example of a function that fails the vertical line test?

Back

A circle is an example of a relation that fails the vertical line test because a vertical line can intersect it at two points.

Front

What is an example of a function that passes the vertical line test?

Back

A linear function, such as y = 2x + 3, passes the vertical line test because each x-value corresponds to exactly one y-value.

Front

What does it mean if a function has a restricted domain?

Back

A restricted domain means that not all possible x-values are included; only certain values are allowed.