Read the entry directions carefully!

The purpose of this question is to do the preliminary work to make a well-labeled sketch of the graph of the function $\displaystyle {f{{\left({x}\right)}}}=\frac{{{4}{x}^{{2}}+{20}{x}+{32}}}{{{x}^{{2}}+{5}{x}-{24}}}$

First, find the critical values (there should be three):
Preview Question 6 Part 1 of 5  

Two of the critical values should be associated with asymptotes of this function. The remaining critical value should be a local maximum. What is the local maximum for this graph:
$\displaystyle {x}=$ Preview Question 6 Part 2 of 5  
$\displaystyle {y}=$ Preview Question 6 Part 3 of 5  

In addition to the vertical asymptotes, there is another asymptote.
Give the equation for this asymptote: Preview Question 6 Part 4 of 5  
Hint: What is $\displaystyle \lim_{{{x}\rightarrow\pm\infty}}{f{{\left({x}\right)}}}$?

Finally, give the range for the function $\displaystyle {f}$.
range = Preview Question 6 Part 5 of 5  

While it will not be graded here, you should also make a well-labled sketch of the function $\displaystyle {y}={f{{\left({x}\right)}}}$.