Let $\displaystyle {f{{\left({x}\right)}}}={\left\lbrace\begin{array}{ccc} \frac{{7}}{{{x}+{9}}}&\text{if}&{x}<-{8}\\{7}&\text{if}&{x}=-{8}\\-\frac{{21}}{{{x}+{5}}}&\text{if}&{x}>-{8}\end{array}\right.}$

Compute the quantities below. Write "DNE" if the limit does not exist or the value is undefined.

$\displaystyle \lim_{{{x}\to-{8}^{{-}}}}{f{{\left({x}\right)}}}=$ Preview Question 6 Part 1 of 6  

$\displaystyle \lim_{{{x}\to-{8}^{+}}}{f{{\left({x}\right)}}}=$ Preview Question 6 Part 2 of 6  

$\displaystyle {f{{\left(-{8}\right)}}}=$ Preview Question 6 Part 3 of 6  

Since the above three quantities are Select an answer all defined and equal defined but not all equal not all defined , we know that $\displaystyle {f}$ is Select an answer discontinuous continuous at $\displaystyle {x}=-{8}$.

List ALL numbers at which $\displaystyle {f}$ is discontinuous. Be sure to check the functions defined to the left and right of -8 for discontinuities. Preview Question 6 Part 6 of 6