Discontinuities.

[modest moss]

easy shortcut for discontinuity is basically whenever the line:
if you see any kind of interruption in a line its discontinuous

• doesnt have a limit, or limit doesnt match actual position of a point
• line literally jumps (like in stepwise function)
• line takes a hard turn (imagine stuff like the vertex in an absolute value function)
• asymptote

there might be more than that but those are pretty much the common stuff

[merry raft]

Understood, and what about the removable or essential discontinuities types?

[modest moss]

the picture you posted counts as discontinuous

im kinda rusty now after a month of not doing limits but the removable can be determined with equation stuff

I think its mostly about re-arranging things so you dont get stuff like dividing by 0

actually it might totally be centered around not dividing by 0

[merry raft]

The thing is, I could carry out a solution with the equations, but what happens is that in this exercise we were not given any equation, it is all at a glance and that is why it is to identify and not resolve something itself with a numerical value.

[modest moss]

we call it "nonremovable discontinuity" idk if thats the same as essential but its whenever its just not possible to get it to work at a certain point even after rearranging

[merry raft]

When you mean a sudden turn, could it be something like this?

[modest moss]

nah those are all smooth enough

[merry raft]

I guess it is the same.

[modest moss]

its whenever you see a point and you just know that you cant really take a proper slope because the limits on both sides would not have the same slopes

I think this kind of turn counts as a "sharp turn"

[merry raft]

I can send the complete exercise, the point is that I don't need the answer as such (which, although it would be useful, is not the idea), as I say, I want to understand the topic. Isn't there a problem with that?