Question

Show all work such as a table on finding the domain and range of L(x)= (x-1)/(x+3)

Answer 1

Answer:

$\begin{gathered} Domain:(-\infty,-3)\cup(-3,\infty) \\ Range:(-\infty,1)\cup(1,\infty) \end{gathered}$

Explanation:

Given the function:

$l(x)=\frac{x-1}{x+3}$

Domain

The domain of a function is the set of the values of x at which the function is defined.

A rational function is undefined when its denominator equals 0.

$\begin{gathered} x+3=0 \\ x=-3 \end{gathered}$

Therefore, the domain of l(x) is:

$(-\infty,-3)\cup(-3,\infty)$

Range

The range of a function is the set of the values of L(x) at which the function is defined.

Since L(x) is a rational function, find the horizontal asymptote.

$Horizontal\;Asymptote,y=1$

Therefore, the range of the function is:

$(-\infty,1)\cup(1,\infty)$