This week we learned about continuity. We also talked more about limits. Talking more about limits cemented it more in my mind. I do not really like talking about continuity when it comes to piecewise functions. Piecewise function annoy me in general and then looking at them closer is just even more annoying. The 3 steps that we use to figure out if something is continuous are actually fairly easy. I like having rules telling me what to do for something like this. It makes me hate math a little bit less. I am still having trouble with being able to look at a graph and being able to tell whether or not it is continuous. Like I feel like piecewise functions should not be continuous but they are. At least I think they are. Are they? Anyway they just confuse me. Also the thing with the graph with vertical asymptotes. Is that continuous? I thought it wasn’t but I think in class we said that it was because the asymptote wasn’t in the domain. So is that it then? Like if there is something that has an asymptote at x=0 so zero isn’t in the domain, it would still be continuous. But it wouldn’t be continuous on the interval [-1,1] because then zero would be in that set of numbers. I guess that makes sense. Okay then I think I’m pretty okay with this now.
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