Basic Technical Mathematics, 11th Edition

3.2 More about Functions

• Domain and Range • Functions from Verbal Statements • Relation

For a given function, the complete set of possible values of the independent variable is called the domain of the function, and the complete set of all possible resulting values of the dependent variable is called the range of the function.

NOTE

[This means there may be restrictions as to the values that may be used since values that lead to division by zero or to imaginary numbers may not be included in the domain or the range.]

As noted earlier, we will use only real numbers when working with functions.

EXAMPLE 1 Domain and range

The function $f(x)\hspace{0.17em}=\hspace{0.17em}{x}^2\hspace{0.17em}+\hspace{0.17em}2$ is defined for all real values of x. This means its domain is written as all real numbers. However, ...