I am learning precalculus and my precalculus book gives this equation:
for this graph:
But when I enter that equation into some online graph tool like Symbolab ( ) I get this graph:
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?
$\endgroup$ 02 Answers
$\begingroup$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.
$\endgroup$ 1 $\begingroup$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 $x=0$.
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