Can someone please explain #5 and #8 to me?

For #5, I get that plugging in -0.66 into the online calculator will give me the y value but I do not understand the rest.

For #8, I get that you can plug in x = -1 because it is a plug-in limit but I do not know which Limit Law(s) to say I used.

Any help would be greatly appreciated!

Thanks in advance!