Domain and Range of Functions

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 do you determine the domain of a function from its graph?

Back

The domain can be determined by identifying the x-values for which the graph exists. Look for any breaks, holes, or vertical asymptotes.

Front

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

Back

The range can be determined by identifying the y-values that the graph reaches. Look for the highest and lowest points on the graph.

Front

What does it mean if a function has a domain of (-∞, 2]?

Back

It means that the function is defined for all x-values less than or equal to 2.

Front

What does it mean if a function has a range of [-2, 10]?

Back

It means that the output values of the function are between -2 and 10, inclusive.

Front

What is an example of a function with a domain of [0, ∞)?

Back

An example is the function f(x) = √x, which is defined for all non-negative x-values.

Front

What is an example of a function with a range of (0, ∞)?

Back

An example is the function f(x) = e^x, which produces only positive output values.

Front

What is the domain of the function f(x) = 1/x?

Back

The domain is all real numbers except x = 0, or (-∞, 0) ∪ (0, ∞).

Front

What is the range of the function f(x) = x^2?

Back

The range is [0, ∞) since the output is always non-negative.