# How do you find all the asymptotes for # (3x )/ (x+4) #?

##### 1 Answer

Mar 27, 2016

vertical asymptote x = -4

horizontal asymptote y = 3

#### Explanation:

Vertical asymptotes occur as the denominator of a rational function tends to zero. To find the equation , let the denominator equal zero.

solve : x + 4 = 0 → x = -4 is the asymptote

Horizontal asymptotes occur as

#lim_(xto+-oo) f(x) → 0# divide terms on numerator/denominator by x

→

#((3x)/x)/(x/x + 4/x) = 3/(1 + 4/x) # as

# x tooo , 4/x to 0#

#rArr y = 3/1 = 3 " is the asymptote " # Here is the graph of the function.

graph{(3x)/(x+4) [-20, 20, -10, 10]}