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

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Answer 1 · 2016-11-03T20:50:18

The Vertical Asymptotes are: $x=1/4 and x=-2$

The Horizontal Asymptote is $y=0$

There is $No$ Oblique Asymptote.

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

$4x^2+7x-2=0$
$rArr(4x-1)(x+2)=0$

$4x-1=0$
$rArr4x=1$
$rArrx=1/4$

$x+2=0$
$rArrx=-2$

The Vertical Asymptotes are: $color(red)(x=1/4 and x=-2)$

Because the degree of numerator is less than the denominator

So, $color(red)(y=0 )$ is the Horizontal Asymptote

There is $color(red)(No)$ Oblique Asymptote.

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