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What are the vertical and horizontal asymptotes of #f(x)=(3x-1)/(x+4)#?

Answer 1

Horizontal Asymptote: #y=3#
Vertical Asymptote : #x=-4#

Since we have to find a vertical Asymptote, we must find a x value that makes the function of form anything/0 since it reaches to infinity. See in the denominator #x=-4# will do something like anything over zero. So #x=-4# is a vertical Asymptote.

For horizontal Asymptote. We must figure out what happens to the function when it reaches infinity. Since we can't figure what happens to the function right in this form. So we must do some tricks. Recall #1/oo rarr 0#. It works for every number Given #f (x)=(3x-1)/(x+4)# Divide numerator and denominator by x . #=[(3/x)-(1/x)]/[(x/x)+(4/x)]# #=(3-1/x)/(1+4/x)# When #x rarr oo# the number with denominator will shrink down to zero #=(3-0)/(1+0)# #=3/1# Hence #y=3# Is the horizontal Asymptote.

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Answer 2

Ethan Adkins

The vertical asymptote of f(x)=(3x-1)/(x+4) is x=-4. There is no horizontal asymptote.

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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.