Let $\displaystyle {f{{\left({x}\right)}}}={\left\lbrace\begin{array}{ccc} \frac{{6}}{{{x}+{3}}}&\text{if}&{x}<-{2}\\-\frac{{24}}{{{x}-{2}}}&\text{if}&{x}>-{2}\end{array}\right.}$

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

$\displaystyle \lim_{{{x}\to-{2}^{{-}}}}{f{{\left({x}\right)}}}=$ Preview Question 6 Part 1 of 6  

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

$\displaystyle {f{{\left(-{2}\right)}}}=$ Preview Question 6 Part 3 of 6  

Since the above three quantities are Select an answer defined but not all equal not all defined all defined and equal , we know that $\displaystyle {f}$ is Select an answer discontinuous continuous at $\displaystyle {x}=-{2}$.

List ALL numbers at which $\displaystyle {f}$ is discontinuous. Be sure to check the functions defined to the left and right of -2 for discontinuities. Preview Question 6 Part 6 of 6