



 
Hi Sarah, I would plot the three functions \begin{eqnarray*} on the same piece of paper and then erase the parts of the graphs that fall outside the appropriate ranges. I will plot $p(x)$ and $q(x).$ I put a red dot on $p(x) = x2$ at $(2, 4)$ since $f(x)$ is only equal to $p(x)$ for $x < 2.$ Erase the portion of the line $y = p(x)$ to the right of the red dot. I put dots on the parabola $q(x) = x^2 4$ at $x = 2$ and $x = 2$ since these points mark the ends of the interval where $f(x)$ coincides with $q(x).$ Erase the portions of the parabola that are outside the domain $2 \leq x \leq 2.$ Now add the third function $r(x) = x+2$ and erase the part not in the domain of $f(x).$ Can you tell from the resulting graph the range of $f(x)?$ Penny  


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