I am learning precalculus and my precalculus book gives this equation:

equation 1

for this graph:


But when I enter that equation into some online graph tool like Symbolab ( https://www.symbolab.com/graphing-calculator ) I get this graph:

graph from symbolab

It seems that (many) online calculators cancel (x+1)(x-1) in numerator/denominator before drawing a graph.

So, which graph of those 2 is "correct"? Why?

P.S. My previous question was downvoted and removed as "not interesting for math community". That was very rude having in mind that I am beginner, looking for a help. Perhaps I should join some other forum for math beginners but I don't know which and where?


The given diagram appears to be a graph of the function $$g(x)=\frac{2x^2-1}{x^2-1}$$ Although the supplied function is $$f(x)=\frac{2(x^2-1)}{x^2-1}=2\qquad\forall x\in\mathbb{R}\setminus\{-1,1\}$$ so the second diagram is correct.

  • $\begingroup$ Yes, that makes sense. Thank you. $\endgroup$ – Milan Che Aug 18 at 20:20

If $x$ equals $-1$ or $1$, $\frac{2x^2-2}{x^2-1}$ does not exist. Otherwise, it is perfectly fine to divide top and bottom by $x^2-1$. That yields the second graph: $y=2$ with gaps at $x=\pm1$.

I will second Peter Foreman's guess at the function of $\frac{2x^2-1}{x^2-1}$. The first graph appears to have asymptotes at $x=\pm1$ and $y=2$. $\frac{2x^2-1}{x^2-1}=2+\frac1{x^2-1}$ can get close to $2$ without ever equaling it and is equal to $1$ at $x=0$.

  • $\begingroup$ If 𝑥 does not equal −1 or 1, the fraction does not exist Don't you mean that the fraction does not exist if x DOES equal -1 or 1? $\endgroup$ – numbermaniac Aug 19 at 5:13
  • 1
    $\begingroup$ @numbermaniac oops. Easy fix. $\endgroup$ – Mike Aug 20 at 4:39

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