Hi, I just want to make sure that I have the correct answer.
(a) 5
(b) 5
(c) 5
(d) 3
(e) 3
(f) 3
There is no limit at $\displaystyle 2$. You can easily see in the graphic that the broken curves (the ones on the right and left hand sides of $\displaystyle 2$) does not become arbitrarily closer to each other at $\displaystyle 2$ (as it happens for $\displaystyle 1$).
I guess Plato made a typo, check your answer for d, it must be $\displaystyle -2$.
Check the lines above by following the color order: red, yellow, green, blue and pink, as the vertical lines approach to $\displaystyle 2$ from left, the horizontal lines approach to $\displaystyle -2$.