How do you graph y=(5x+2)/(4x) using asymptotes, intercepts, end behavior?

Feb 19, 2017

Asymptotes : $x \left(y - \frac{5}{4}\right) = 0$. x-intercept ( y = 0 ) : $- \frac{2}{5}$. No intercepts at all. See asymptotes-inclusive Socratic graph.

Explanation:

graph{(x(y-5/4)-1/2)(y-5/4+.001x) (x--.001y)=0 [-5, 5, -2.5, 2.5]}

This is $y = \frac{5}{4} + \frac{1}{2 x}$, giving

$\left(y - \frac{5}{4}\right) \left(x\right) = \frac{1}{2}$, representing the rectangular hyperbola,

with center at C( 0, 15/4) , at which the asymptotes

$x \left(y - \frac{5}{4}\right) = 0$ intersect.

x-intercept ( y = 0 ) : $- \frac{2}{5}$

There are no intercepts at all.