What are the asymptote(s) and hole(s), if any, of # f(x) = (x*(x-2))/(x^2-2x+1)#?

Answer 1

#x=1" "# is the vertical asymptote of #f (x)#.
#" "#
#y=1" "# is the horizantal asymptote of #f (x)#

This rational equation has a vertical and horizantal asymptote . #" "# Vertical asymptote is determined by factorizing the denominator : #" "# #x^2-2x+1# #" "# #=x^2-2 (1)(x)+1^2# #" "# #=(x-1)^2# #" "# Then,#" "x=1" "#is a vertical asymptote. #" "# Let us find the horizantal asymptote : #" "# As it is known we have To check both degrees of the #" '# numerator and denominator . #" "# Here , the degree of the numerator is #2# and that of the #" "# denominator is #2# too . #" "# If #(ax^2+bx+c)/(a_1x^2+b_1x+c_1)#then the horizantal asymptote is #color (blue)(a/(a_1))# #" "# In #f (x)=(x. (x-2))/(x^2-2x+1)=(x^2-2x)/(x^2-2x+1)# #" "# Same degree in the numerator and denominator then horizantal #" "# asymptote is #y=color (blue)(1/1)=1# #" "# #therefore x=1 and y=1 " "# are the asymptotes of #f (x)#.
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

The function f(x) = (x*(x-2))/(x^2-2x+1) has a vertical asymptote at x = 1 and a hole at x = 2.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7