How do you determine the vertical and horizontal asymptotes of the graph of each function #f(x) = (3x)/(x+4)#?

1 Answer
Aug 19, 2015

Answer:

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

Explanation:

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

Step 1. Find the vertical asymptotes.

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

#x+4=0#

#x=-4#

There is a vertical asymptote at #x=-4#.

Step 3. Find the horizontal asymptotes.

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

#3/1=3#

The horizontal asymptote is at #y=3#.

Graph