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Continuous and Discontinuous Functions

vanillabean
in Homework Help

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I have attached the question in a file to this post. I am taking an online calc 1 course and I am struggling with this concept of continuous and discontinuous functions. I know the answer to this question is b, but I do not understand why. I've spent a couple hours (yeah :( ) on trying to understand this problem but I STILL DON'T GET IT. Can someone explain it to me? Online videos are unhelpful and my textbook is not doing it for me.

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