2a. Domain and Range of a Function

Definitions of Domain and Range

Domain: The complete set of possible values of the independent variable in a function is called the domain of the function.

In plain English, the definition means:

The domain of a function is all the possible x values which will make the function "work" by outputting real values.

When finding the domain, remember:

denominator (bottom) of a fraction cannot be zero

the values under a square root must be positive

Range: The complete set of all possible resulting values of the dependent variable in a function is the range of the function.

In plain English, the definition means:

The range of a function is the possible y values of a function resulting when we substitute all the possible x-values.

When finding the range, remember:

substitute different x-values into the expression for y to see what is happening

make sure you look for minimum and maximum values of y

draw a sketch!

Because real numbers are used in the domain and range of a function, values that lead to division by zero or to imaginary numbers are not included.

Imaginary Numbers

An imaginary number is the result of finding the square root of a negative number. [Your calculator may give you an ERROR message if you try to do this, but it is still possible.]

Imaginary numbers have applications in electronics.

Example

√(-4) = 2j

The number 2j is an imaginary number.