How do you find vertical and horizontal asymptotes of #(4x)/(x-3)#?

1 Answer
Aug 19, 2015

Answer:

There is a vertical asymptote at #color(red)(x=3)# and a horizontal asymptote at #color(red)(y=4)#.

Explanation:

#f(x)=(4x)/(x-3)#

Step 1. Find the vertical asymptotes.

Set the denominator equal to zero and solve for #x#.

#x-3=0#

#x=3#

There is a vertical asymptote at #x=3#.

Step 3. Find the horizontal asymptotes.

Since the numerator and denominator are the same degree, we must divide the coefficients of the highest terms.

#4/1=4#

The horizontal asymptote is at #y=4#.

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