How do you find the asymptotes for y= (7x-2) /( x^2-3x-4)?

Jan 14, 2016

The asymptotes of any expression are found by defining what happens to the expression when $x \to \infty$ or $x \to - \infty$ or when $y \to \infty$
The asymptotes of any expression are found by defining what happens to the expression when $x \to \infty$ or $x \to - \infty$ or when $y \to \infty$
In this case $y = \frac{7 x + 2}{{x}^{2} - 3 x - 4}$ or $\frac{7 x - 2}{\left(x - 4\right) \left(x + 1\right)}$
Hence when $x \to 4$ or $x \to - 1$ then $y \to \infty$. Therefore there are vertical asymptotes at $x = 4$ and at $x = - 1$
${\lim}_{x \to \pm \infty} \frac{7 x - 2}{{x}^{2} - 3 x - 4} = {\lim}_{x \to \pm \infty} \frac{7}{x} = 0$