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\question % workshop bank Ch. 2 -> esergel26
Recall that a function $f$ is continuous at the point $c$ if $\displaystyle \lim_{x \to c} f(x) = f(c)$. Complete the definition of $f(x)$ below so that $f$ is continuous at every point. Then sketch the graph of your function $f(x)$.
$$
f(x) = \begin{cases}
2x^2+2 &\hbox{if } x<1 \\
\phantom{   \displaystyle \frac{10}{x} + \frac{10}{x} + \frac{10}{x} } &\hbox{if } 1 \leq x \leq 2 \\
\displaystyle 2 - \frac{6}{x} &\hbox{if } x>2.
\end{cases}
$$

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