I was graphing
$$y=\frac{x^{\frac{1}{3}}-4^{\frac13}}{x^2-8x+16}$$
and
$$y=\frac{x^{\frac{1}{3}}-4^{\frac13}}{(x-4)^2}$$
but they seemed to differ at $x=4$ as shown in the picture. Why is that?
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I only see one function graphed there, which might indicate the other is equal. – Thomas Andrews Sep 24 '21 at 02:23
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@ThomasAndrews the green function has the denominator expanded while the orange has it in the form (a+b)^2 – kenobiii Sep 24 '21 at 02:28
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1The way graphing calculators and computers "graph" a function is by plugging in values, evaluating, and then plotting those points, joining them under the assumption that the function is continuous. Because computers do not have "infinite precision", these calculations often involve rounding in sundry ways. The calculation of $(a+b)^2$ is performed differently from the calculation of $a^2+2ab+b^2$: there are more operations in the latter case, and more possibility of rounding errors in the approximation. So it would not be a surprise if you don't always get the exact same values. – Arturo Magidin Sep 24 '21 at 02:33