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I noticed how tangent and cubic functions both produce cubic graphs. What exactly is the relationship between them?

Marwi
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    The graph of $\tan$ is far from rensembling a cubic. –  Jul 30 '20 at 19:44
  • Welcome to Maths SX! How did you notice that? A cubic function has no vertical asymptote, and is no periodic. – Bernard Jul 30 '20 at 19:44
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    Maybe what you are referring to is its resemblance with a high degree odd polynomial, which can explained by its taylor expansion: $$x+\frac 13 x^3 +\frac{2}{15}x^5\cdots$$ – Vishu Jul 30 '20 at 19:46
  • I apologize for the confusion. I meant that when you graph $f(x)=\tan(x)$ and $f(x)=x^3$ as an example, they both have that cubic shape. Based on your comments, I assume it just looks like a cubic but it’s not technically a cubic. – Marwi Jul 30 '20 at 19:56

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If you sketch the graph by hand, both the graphs appear to be same. But, here's the actual graph. Note that, $\tan x$ has vertical asymptotes at $x=\pm π/2$ and rapidly increases after $x=π/4$. Also, see the curvature of both the graphs, they are different.

SarGe
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