Continuity of piecewise functions (limit as x -> 1)

[coooool222]

The answer key is telling me that it is continuous except x=1 and x=-4. I think this is false due to the fact that

Isn't it continuous if both limits on the write and left side equal, and also equal to the functions value.

 

[Dr.Peterson]

View attachment 34715
The answer key is telling me that it is continuous except x=1 and x=-4. I think this is false due to the fact that
View attachment 34716
Isn't it continuous if both limits on the write and left side equal, and also equal to the functions value.

You're saying you believe it is continuous at x=1, right?

But f(1) is not defined:

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So your claim can't be true!

On the other hand, at x=4, the function is defined, but the limit does not exist.

 

[coooool222]

oh yeah 1 does not equal to x