Recall that a function $f$ is continuous at a number $a$ if the following holds. $\underset{xa}{lim}f(x)=f(a)$ We are given the following. $f(x)=\{\begin{array}{ccc}c{x}^2+3x& if& x<2\\ x^3-cx& if& x2\end{array}$ We note that for all values of the constant $c$ the function $f$ is continuous on both $(-,2)$ and $(2,).$ The only case that we need to consider is when $x=2.$ For the function $f$ to be continuous on $(-,),$ we need to ensure that there is not a discontinuity at $x=2.$ To do so$,$ we must deter