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# Sketching the graph for y = 1/x-1 +1/x+1. watch

1. I know it will have vertical asymptotes at x = 1 and x = -1 and that it will approach 0 as . But I am not sure how to determine whether y tends to 0 from above/below the x-axis, as well as what happens for -1<x<1.
2. (Original post by FXLander)
I know it will have vertical asymptotes at x = 1 and x = -1 and that it will approach 0 as . But I am not sure how to determine whether y tends to 0 from above/below the x-axis, as well as what happens for -1<x<1.
For infinities, consider whether each of the terms is +ve or -ve, for large values +ve and large values -ve.

Between -1 and 1, plotting a few points is probably easiest. Alternatively consider what happens as x goes up to 1, what are the signs and relative sizes of the two terms - are they both bounded? Does one go off to infinity? Plus or minus?. Similarly as x goes down to -1.

And plot the point for x=0.
3. (Original post by FXLander)
I know it will have vertical asymptotes at x = 1 and x = -1 and that it will approach 0 as . But I am not sure how to determine whether y tends to 0 from above/below the x-axis, as well as what happens for -1<x<1.
If you say that then you can examine what happens as . If it approaches from the LEFT, then and so the numerator is negative, while the denominator is positive (since for ). So you essentially get negative/positive which is still negative. So as , we know that

Repeat similar analysis for , and

As for what happens when , then consider the form above again, and branching from the last thing I said. We know that and for the first half of the interval, so here. Then for the second half. So as you go from to your should go from positive to negative while crossing the origin.

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