Chapter 2.3, Problem 78E

Graph the function given by

$f\left(x\right)=\frac{\sqrt{x^2+3x+2}}{x-3}$.

a. Estimate $\underset{x\to \infty }{\lim }f\left(x\right)$ and $\underset{x\to -\infty }{\lim }f\left(x\right)$ using the graph and input–output tables as needed to refine your estimates.

b. What appears to be the domain of the function? Explain.

c. Find $\underset{x\to -2^{-}}{\lim }f\left(x\right)\text{ and }\underset{x\to -1^{+}}{\lim }f\left(x\right)$.