Please help with 1921 and 13 Please show work Thanks a bunch

Please help with 19-21, and 13

Please show work. Thanks a bunch.

Solution

y=x³/(2x²-2)

19) degree of numerator is more than degree of denominator ,so no horizontal asymptotes

for vertical asymptotes , denominator =0

2x²-2=0

2x²=2

x²=1

x=-1,x=1 are vertical asymptotes

20)y=f(x)=x³/(2x²-2)

f(-x)=(-x)³/(2(-x)²-2)

f(-x)=- x³/(2x²-2)

f(-x)= - f(x)

so function is odd

graph of function is odd

21) only considering highest degrees in numerator , denominator of y=x³/(2x²-2)

y=x³/(2x²)

y=x/2

graph has same end behaviour as that of y=x/2