HW8 Problem 8 Previous Problem List Next to indicate a horiz

HW8: Problem 8 Previous Problem List Next to indicate a horizontal asymptote other than the z axis, \"v to (1 point) For the following functions, use \"x to indicate that the z-axs is an asymptote. h indicate a vertical asymptote, \"s\" t indicate them all in alphabetical order. (For example, if a function has a vertical asymptote and slant asymptote, then submit sv) to indicate a slant asymptote, and \'n\" the lack of an asymptote. If the graph of a function has several types of asymptotes h,v h,v x.v (r-1) (z-1) 1@- Note: You can earn partial credit on this problem. Submit Answers Preview My Answers You have attempted this problem 53 times Your overall recorded score is 25%. You have unlimited attempts remaining Email instructor

Solution

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

horizontal asym. : degree of den. is greater than num. so, x axis is the horizaontal asymtote.

-------- x

vertical asymtote : plug den. =0

x=1 ---- v

So, Option : v, x

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

horizontal asym. : degree of den. is equal to degree of num. so, horizaontal asymtote.

y =x^2/x^2 = 1

-------- h

vertical asymtote : plug den. =0

(x-1)^2 =0 ; x=1

------- v

Option : h , v

3) f(x) = x^3/(x-1)^2

Degree of num is > degree of denominator.So, no horizaontal asymtote but slant asymtote

exists

----- s

vertical asymtote : plug den. =0

(x-1)^2 =0 ; x=1

------ v

Option : s , v

4) f(x) = x^2/(x^2 +1)

Horizontal asymtote : y = x^2/x^2

y = 1

------ h

Vertical asymtote: None

Option : h