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April 9th, 2017, 11:59 PM   #1
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How to distinguish between these two graphs?

Consider the two functions f(x) = x^2 and g(x) = 1/|x|.

The first one is a parabola with the vertex at the origin. The second one is an absolute value function with a V-shaped graph.

If you take the reciprocal of both functions, their graphs look very similar.
Both have an asymptote along each axis and their curves are in quadrants one and two.

If you just see their reciprocal graphs, how can you tell which graph is represented by which reciprocal function?

Can someone explain this? Thanks a lot.
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April 10th, 2017, 12:29 AM   #2
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look at the point $x=\dfrac 1 2$
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