# How do you find the asymptotes for #(3x-12)/( 4x-2)#?

##### 2 Answers

Horizontal asymptotes of a rational function occurs when the function in the denominator becomes zero.

In this case the function in denominator is

For horizontal asymptotes

Hence horizontal asymptote is

Vertical asymptotes accurs when the degree of numerator and denominator is equal. In this case both numerator and denominator have a degree

In this case the leading coefficients of numerator and denominator are

#### Answer:

vertical asymptote at

# x = 1/2 #

horizontal asymptote at y =#3/4 #

#### Explanation:

Vertical asymptotes can be found when the denominator of

the rational function is zero.

This will be when : 4x - 2 =0 hence 4x = 2 so x

# = 1/2 # [ Horizontal asymptotes can be found when the degree of the

numerator and the degree of the denominator are equal ]

In this question they are both of degree 1 and so equal.

The asymptote can be found by taking the ratio of leading

coefficients hence y =

# 3/4 #

graph{(3x-12)/(4x - 2) [-22.5, 22.5, -11.25, 11.25]}