Question

function with the following limit properties. 16. $lim_{x
ightarrow - 3^{-}}f(x)=6$ $lim_{x
ightarrow - 3^{+}}f(x)=6$ $lim_{x
ightarrow - 1^{-}}f(x)=+infty$ $lim_{x
ightarrow - 1^{+}}f(x)=+infty$

Explanation:

Step1: Analyze left - hand and right - hand limits at $x=-3$

Since $\lim_{x
ightarrow - 3^{-}}f(x)=6$ and $\lim_{x
ightarrow - 3^{+}}f(x)=6$, the two - sided limit $\lim_{x
ightarrow - 3}f(x)=6$.

Step2: Analyze left - hand and right - hand limits at $x = - 1$

Since $\lim_{x
ightarrow - 1^{-}}f(x)=+\infty$ and $\lim_{x
ightarrow - 1^{+}}f(x)=+\infty$, there is a vertical asymptote at $x=-1$. A possible function is $f(x)=\frac{6}{(x + 1)^2}+6$.

Answer:

A possible function is $f(x)=\frac{6}{(x + 1)^2}+6$