# How do you find the asymptotes for #1. f(x) = (3x) / (x+4)#?

##### 2 Answers

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 equation

Horizontal asymptotes occur as

#lim_(x→±∞) f(x) → 0# If the degree of the numerator and denominator are equal , as is the case here , both of degree 1. The equation can be found by taking the ratio of the leading coefficients.

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

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

Just another way of looking at the same thing

#### Explanation:

Given:

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Lets 'get rid' if the

Straight away you can observe that the denominator is 0 when

As absolute