I need some help on a few problems tonight. Here's the first one. Putting these problems in screenshot form since there is quite a bit of info or graphs involved with each. https://gyazo.com/616cea451186eae7a3eff2052bdd5f49

Question

tkhunny · Answer

What does "continuous" mean?

anonymous · Answer

It means that there are no breaks in the function when graphed, at least over that interval, right?

mathmale · Answer

Right.  In practical terms, it also means that where the function formula changes (in this case, at x=1), the value y of the piecewise function does not change suddenly; there are no gaps between graphs.  See the example following:|dw:1454475790976:dw|

anonymous · Answer

So then, the answer would be that B=6 because where x=1, there is no sudden change in the y-value like in the form of a jump? I say B=6 because I put in both equations into my graphing calculator, traced for x=1, and it turned out to be y=6, which is where both graphs seem to cross on this interval.

anonymous · Answer

Oh, I got it right. Not sure if I have quite the right thinking, but I'm sure I can piece enough together to get it right from now on. Thank you. :)