How to find the asymptotes of f(x) = (x+2) /( 2x-5)?

Jan 15, 2016

The asymptotes can be found by looking at ${\lim}_{x \to \infty}$ , ${\lim}_{x \to - \infty}$ and lim_(f(x)->oo
The asymptotes can be found by looking at ${\lim}_{x \to \infty}$ , ${\lim}_{x \to - \infty}$ and lim_(f(x)->oo
Looking at the last one first, $f \left(x\right) \to \infty$ as the denominator approaches zero. This occurs when $2 x \to 5$. This means there is a vertical asymptote at $x = \frac{5}{2}$
As $x$ gets very large, either negatively or positively, $\frac{x + 2}{2 x - 5} \to \frac{x}{2 x} \to \frac{1}{2}$
Thus there is a horizontal asymptote at $y = \frac{1}{2}$