How do you find the horizontal asymptote for #f(x) = (3x) / (x+4)#?

Answer 1

I found #y=3#

The horizontal asymptote is a line towards which the curve, described by your function, tends to get as near as possible.

To find it you can try to see what happens to your function when #x# becomes VERY big....and see if your functions "tends" to some kind of fixed value: as #x# becomes very big, say #x=1,000,000# you have: #f(1,000,000)=(3*1,000,000)/(1,000,000+4)# let us forget the #4# that is negligible compared to #1,000,000#; you have:
#f(1,000,000)=(3*cancel(1,000,000))/(cancel(1,000,000))=3#
So when #x# becomes very big positively (and negatively, you can try this) your functions "tends" to get near the value #3#! So the horizontal line of equation #y=3# will be your asymptote!

You can plot your function and see this tendency! graph{(3x)/(x+4) [-41.1, 41.07, -20.56, 20.53]}

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 horizontal asymptote for the function ( f(x) = \frac{3x}{x+4} ), you need to examine the behavior of the function as ( x ) approaches positive or negative infinity.

For rational functions like this one, if the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is at ( y = 0 ).

In this case, the degree of the numerator is 1 and the degree of the denominator is also 1. To find the horizontal asymptote, divide the leading coefficient of the numerator by the leading coefficient of the denominator:

[ \lim_{x \to \pm \infty} \frac{3x}{x+4} = \frac{3}{1} = 3 ]

So, the horizontal asymptote of ( f(x) ) is ( y = 3 ).

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