Use the following to indicate

Question

For the following functions, use "x" to indicate that the x-axis is an asymptote, "h" to indicate a horizontal asymptote other than the x axis, "v" to indicate a vertical asymptote, "s" to indicate a slanted asymptote, and "n" the lack of an asymptote. If the graph of a function has several types of asymptotes indicate them all in alphabetical order. (For example, if the x-axis was an asymptote and there was a vertical asymptote, you would enter vx without a comma between them.) 

 f(x)=x(x−1)2. 

 f(x)=x2(x−1)2. 

 f(x)=x3(x−1)2. 

 f(x)=x2x2+1. 

Answer 1

y=x(x-1)^2=x(x^2-2x+1)= x^3-2x^2+x

upside down U coupled to U

no asymptotes

you might try graphing these functions

2nd is UU or W shaped

n

n

n

n

UNLESS you might have meant to write

f(x) = x/(x-1)^2

with / signs, you get asymptotes, horizontal and vertical, and one slant

for x/(x-1)^2, x=1 is a vertical asymptote, y=0 is the horizontal asymptote

xv

for x^2/(x-1)^2, same vertical, but y=1 is the horizontal

hv

for x^3/(x-1)^2, same vertical, but y=x is slanted asymptote

sv

so

xv

hv

sv

? maybe h, not sure what you mean by f(x) = x^2x^2+1

maybe you mean x^2/(x^2+1)? if so, then

y=1 is the horizontal asymptote, no horizontal or slanted asymptotes