Answer
$$\lim_{x\to-3}f(x)=-6$$
Work Step by Step
$$f(x)=\frac{x^2-9}{x+3}$$
(a) The table is shown below.
As we can see from 2 tables, as $x$ approaches $-3$, the value of $f(x)$ will get closer and closer to $-6$. So a logical estimate would be $\lim_{x\to-3}f(x)=-6$.
(b) The graph is shown below.
Again, looking at the graph, the closer $x$ approaches $-3$, the closer $y$ approaches $-6$. So we ca estimate $\lim_{x\to-3}f(x)=-6$.
(c) $$\lim_{x\to-3}f(x)=\lim_{x\to-3}\frac{x^2-9}{x+3}=\lim_{x\to-3}\frac{(x-3)(x+3)}{x+3}$$ $$=\lim_{x\to-3}x-3=-3-3=-6$$
Therefore, $$\lim_{x\to-3}f(x)=-6$$
