clear handwriting Determine the vertical of the graph of the

clear handwriting

Determine the vertical of the graph of the function. G(x) = x^2/2x^2 - x^2 - 3x Determine the horizontal of the graph of the function. G(x) = x^3 - 2x^2 + x -1/x^2-16

Solution

vertical assymptotes of (x^3)/(2x^3 -x^2 -3x)

for finding vertical assymptotes we will find undefined singularity points

put denominator =0

2x^3 -x^2 -3x=0

x=0,2x^2 -x -3 =0

x=0,x=-1,x=3/2 are vertical assymptotes

2.finding horizontal assymototes of (x^3 -2x^2 +x-1)/(x^2 -16)

degree of numerator =3

degree of denominator =2

degree of numerator> degree of denominator

for rational function slant assymptote is quotient of polynomial division

(x^3 -2x^2 +x-1)/(x^2 -16)

quotient is x-2

remainder is 17x-33

so horizontal assymptote is y=x-2

thank you