Explain why the function is discontinuous at the given number a. (Select all that apply.) f(x) a = -1 x +1 lim f(x) and lim f(x) exist, but are not equal. x-1+ x-1 f(-1) and lim (x) exist, but are not equal. X-1 - lim f(x) does not exist. x-1 V (-1) is undefined. none of the above Sketch the graph of the function.
Hello,
I need to explain why f(x) = 1/(x+1) is discontinuos at the given number a, where a = -1. I initially thought that the only reason for f(x) being discontinuous at a was f(x) being undefined at a, but found that answer to be incorrect. Graphing the equation, I get the graph on the right on the picture attached. I'm confused because the equation seems to go in two different directions without meeting, so I thought that this must mean it's two unequal right hand and left hand limits, which coincides with the other answer choice I selected of the limit of x approaching -1 from both sides not existing. The other two choices can't be correct because there is obviously at vertical asymptote where a = -1, and "None of the above" would make no sense either. What am I doing wrong here?
Thank you
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