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SugarRainbow
how to graph general rational functions? like y=2x/x^2-1
\[y=\frac{2x}{x^2-1}\] \[y=\frac{2x}{(x-1)(x+1)}\] the function will be zero at x=0 so there will be asymptotes at \[x=\pm1\]
when \(0<< x\) (x is a large positive number) the numerator will be large and positive, but the denominator much larger and will dominate, and hence the function will be small when \(x<<0\) (x is large negative number) the numerator will be negative and large, but the denominator will again dominate and hence the function will be small and negative