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Say I have a function $f(x) = x^2 + 2$

This function never touches the x-axis, but it could be easily transformed to touch it by cancelling the constant as in $g(x) = (x^2 + 2) - 2$

Is there any way to generalize this, so that I can make any function "magnet" to the x-axis?

Timmy Diehl
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2 Answers2

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Simply letting $g(x)=f(x)-f(x_0)$ for any $x_0\in\mathbb R$ such that $f$ is well-defined at $x_0$ works

Pearson
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  • If I had $f(x) = x^4 + 3x^3 + 2x^2 + 2$ and I use this method, is works well, but is there any possible way to get the lowest part of the function to touch the x-axis rather than allowing part of it to overflow? – Timmy Diehl Jul 13 '22 at 19:04
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if you mean touching in the sense that the x axes is a tangent o zur graph of f , than f(x9) must have at least one point x0 with f'(x0)=0 then you just take g(x)=f(x)-f(x0) and g touches the x- axes.

trula
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