# How do you find vertical, horizontal and oblique asymptotes for f(x) = (x)/( 4x^2+7x-2)?

Nov 3, 2016

The Vertical Asymptotes are: $x = \frac{1}{4} \mathmr{and} x = - 2$

The Horizontal Asymptote is $y = 0$

There is $N o$ Oblique Asymptote.

#### Explanation:

Finding the vertical asymptote of a rational function is by setting its denominator to zero that is

$4 {x}^{2} + 7 x - 2 = 0$
$\Rightarrow \left(4 x - 1\right) \left(x + 2\right) = 0$

$4 x - 1 = 0$
$\Rightarrow 4 x = 1$
$\Rightarrow x = \frac{1}{4}$

$x + 2 = 0$
$\Rightarrow x = - 2$

The Vertical Asymptotes are: $\textcolor{red}{x = \frac{1}{4} \mathmr{and} x = - 2}$

Because the degree of numerator is less than the denominator

So, $\textcolor{red}{y = 0}$ is the Horizontal Asymptote

There is $\textcolor{red}{N o}$ Oblique Asymptote.