A function is said to have a horizontal asymptote if either the limit at infinity exists or the limit at negative infinity exists.
Show that each of the following functions has a horizontal asymptote by calculating the given limit.

$\displaystyle \lim_{{{x}\to\infty}}\ \frac{{-{12}{x}}}{{{9}+{2}{x}}}=$ Preview Question 6 Part 1 of 5  

$\displaystyle \lim_{{{x}\to-\infty}}\ \frac{{{8}{x}-{2}}}{{{x}^{{3}}+{3}{x}-{2}}}=$ Preview Question 6 Part 2 of 5  

$\displaystyle \lim_{{{x}\to\infty}}\ \frac{{{x}^{{2}}-{4}{x}-{4}}}{{{14}-{11}{x}^{{2}}}}=$ Preview Question 6 Part 3 of 5  

$\displaystyle \lim_{{{x}\to\infty}}\ \frac{{\sqrt{{{x}^{{2}}+{7}{x}}}}}{{{13}-{8}{x}}}=$ Preview Question 6 Part 4 of 5  

$\displaystyle \lim_{{{x}\to-\infty}}\ \frac{{\sqrt{{{x}^{{2}}+{7}{x}}}}}{{{13}-{8}{x}}}=$ Preview Question 6 Part 5 of 5