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.