Classifying the discontinuity at x = 3

First find the one-sided limits at $x=3$. From the left, using $2x+1$: $\lim_{x\to 3^-} y(x) = 2(3)+1 = 7$. From the right, using $x+5$: $\lim_{x\to 3^+} y(x) = 3+5 = 8$.

Since the left-hand limit is $7$ and the right-hand limit is $8$, these two values are unequal, so $\lim_{x\to 3} y(x)$ does not exist even though both one-sided limits exist and are finite. Because both one-sided limits are finite but different, this is a jump discontinuity at $x=3$ (the value $y(3)=7$ is irrelevant to this classification, since the limit itself fails to exist).