Checking the three-part continuity test at x = -1

First evaluate $d(-1)$ directly from the piecewise definition: since $x=-1$ falls in the middle case, $d(-1) = -1$. Next find the left-hand limit using the rule for $x<-1$: $\lim_{x\to -1^-} d(x) = (-1)^2 + 2(-1) = 1 - 2 = -1$. Then find the right-hand limit using the rule for $x>-1$: $\lim_{x\to -1^+} d(x) = 3(-1)+2 = -1$.

Since both one-sided limits equal $-1$, the overall limit exists: $\lim_{x\to -1} d(x) = -1$. Comparing this to $d(-1) = -1$, all three conditions of the continuity definition hold ($d(-1)$ is defined, the limit exists, and the limit equals $d(-1)$), so $d$ is continuous at $x=-1$, with no discontinuity to classify.