Classify the discontinuity of a piecewise function at a breakpoint

First find the one-sided limits at $x=2$. From the left, $h(x) = 3x+1$, so $\lim_{x \to 2^-} h(x) = 3(2)+1 = 7$. From the right, $h(x) = x^2$, so $\lim_{x \to 2^+} h(x) = (2)^2 = 4$.

Since the left-hand limit ($7$) and right-hand limit ($4$) are both finite but not equal to each other, $\lim_{x\to 2} h(x)$ does not exist, and the graph has a break where the two pieces do not meet. Because both one-sided limits are finite (no infinite behavior) but disagree, this is a jump discontinuity at $x=2$.