Explanation:
a) 4
b) 4
c) 4
d) DNE
why is that ? as there is a hollow dot in the curve exactly at x = -3, there is no defined functional value for x = -3.
but it is only this one specific dot that is excluded. so, the lim calculation can still use it for a) - c). although it changes direction there, it is still the same coming from left or from right. and therefore it is the same limit overall.
e) 1
f) -1
g) DNE
h) 1
at x = 0 the function has a jumping discontinuity. therefore, the limits are different when coming from left or from right. and because of this difference, the general limit does not exist. the functional value at x = 0 is part of the curve coming from the left.
i) 2
j) DNE
similar to a) - d). the point (but only the single point) at x = 2 is excluded from the function and has no assigned functional value. nevertheless, it can still be used for the limit calculation.
k) it is not very well to see in the picture. when coming from the right, it appears to be 3.
but it might be possible that it goes further down to 2.
l) similar to k) it is not good to see in the picture. when coming from the left, is the wild "swinging" ending at 2 ? or going back up to 3 to meet the functional curve of k) ?
I would suspect it is 3, but it could be 2.
you need to decide k) and l) when you look at your original, because the picture is too fuzzy to be sure.