How do you find the asymptotes for #f(x) = (x+1) / (x+2)#?

Answer 1

Vertical asymptotes will occur when the denominator is equal to 0 ...

Vertical Asymptote(s) :
#x+2=0#
So, one vertical at #x=-2#

Horizontal asymptote :
There can only be one or none of these. Find it by looking for the greatest exponent in the numerator and denominator. If the exponent is the same for both, then you will have a horizontal asymptote.

For this problem, the greatest exponent is 1 for both, so we have a horizontal:

horizontal : #y=x/x=1#. So, #y=1# is the horizontal.

See the graph below. The dotted lines are the asymptotes.

hope that helped

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

To find the asymptotes of ( f(x) = \frac{x+1}{x+2} ), you need to consider the behavior of the function as ( x ) approaches certain values.

  1. Vertical Asymptotes: Vertical asymptotes occur where the denominator of the function becomes zero, but the numerator does not. In this case, the denominator ( x + 2 ) becomes zero when ( x = -2 ), so there is a vertical asymptote at ( x = -2 ).

  2. Horizontal Asymptotes: Horizontal asymptotes occur when the function approaches a constant value as ( x ) approaches positive or negative infinity. To find horizontal asymptotes, you compare the degrees of the numerator and denominator of the function. If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is at ( y = 0 ). If the degrees are equal, the horizontal asymptote is the ratio of the leading coefficients. If the degree of the numerator is greater, there is no horizontal asymptote.

In this case, both the numerator and denominator have the same degree, which is 1. Therefore, the horizontal asymptote is the ratio of the leading coefficients, which are both 1. So, the horizontal asymptote is ( y = 1 ).

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