Domain and Range

Front

What is the definition of 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 definition of 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

To determine the domain from a graph, identify the x-values for which the graph has points. This includes all x-values where the graph exists.

Front

What does it mean if a function has a domain of all real numbers?

Back

If a function has a domain of all real numbers, it means that there are no restrictions on the input values; any real number can be used as an input.

Front

What is an example of a function with a restricted domain?

Back

An example of a function with a restricted domain is f(x) = √x, which is only defined for x ≥ 0.

Front

What is the domain of the function f(x) = 1/(x-2)?

Back

The domain of f(x) = 1/(x-2) is all real numbers except x = 2, since the function is undefined at that point.

Front

How can you express the domain of a function using interval notation?

Back

The domain can be expressed in interval notation by using brackets [ ] for inclusive endpoints and parentheses ( ) for exclusive endpoints.

Front

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

Back

The range of f(x) = x^2 is all real numbers y such that y ≥ 0, since the output of the function is always non-negative.

Front

What is the significance of vertical lines in determining the domain of a graph?

Back

Vertical lines can be used to test if a graph is a function; if a vertical line intersects the graph at more than one point, it is not a function.

Front

What is the range of the function f(x) = 3x + 2?

Back

The range of f(x) = 3x + 2 is all real numbers, since it is a linear function that can produce any y-value.