Notes: `y=(2x)/(x^2-1)` Graph the function.

Monday, 26 January 2015

$\displaystyle{y}=\frac{{{2}{x}}}{{{{x}}^{{2}}-{1}}}$ Graph the function.

We are asked to graph the function $\displaystyle{y}=\frac{{{2}{x}}}{{{{x}}^{{2}}-{1}}}$ :

Factoring the denominator we get:

$\displaystyle{y}=\frac{{{2}{x}}}{{{\left({x}+{1}\right)}{\left({x}-{1}\right)}}}$

The graph has vertical asymptotes at x=1 and x=-1. The horizontal asymptote is y=0.

The y-intercept is 0 as is the only x-intercept.

The first derivative is $\displaystyle{y}'=\frac{{-{2}{\left({{x}}^{{2}}+{1}\right)}}}{{{{\left({{x}}^{{2}}-{1}\right)}}^{{2}}}}$ so the function is decreasing on its domain.