Chapter 3.6, Problem 34HP

To determine

To find: The domain and range of given linear functions.

Answer to Problem 34HP

For linear function $Ax+By=C$ the domain and range both will be real numbers.

For linear function $a_n=a_1+(n-1)d$ the domain is whole numbers and range is real numbers.

Explanation of Solution

Given information: Linear functions described by $Ax+By=C$ and $a_n=a_1+(n-1)d$ .

Linear functions $Ax+By=C$ represent the general form of a line so $x$ is defined for all real values of $x$ as well as for $y$ so domain and range will be real numbers

whereas $a_n=a_1+(n-1)d$ represent the general form of Arithmetic Progression where $a_1$ is the first term, $d$ is the common difference and $n$ is the number of terms. Since $n$ is defined for any whole number therefore the domain will be a whole number whereas $a_1$ and $d$ will be any real value so therefore range will be any real number.