In the questions, they likely only want you to stipulate whether or not a function approaches positive infinity or negative infinity as x approaches the discontinuity. Here the limit doesn't "equal" infinity, so much that it "does not exist". Assuming we are dealing with asymptotes, approaching the x value of the asymptote from either the left or right will result in either a positive or negative infinity. In rational functions, you can have asymptotes or a "removable" discontinuity. Additionally note that the value of the function exactly at the asymptote is not defined. However the function can reach any arbitrarily large value for any suitably chosen x value (respective of left or right) close to the asymptote. If a function approaches infinity (either positive or negative) as the x-value approaches the asymptote (from the left or right) then the function is unbounded at that point as much as it is undefined at that point. Know this however: you are correct, infinity is not a number, and it cannot used as the value of a limit. Name Three types of Discontinuity.Perhaps you're right and the question and the tutorial are inconsistent. If seen practically if we cannot draw the curve with a single stroke then also it is discontinuous.
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