Question

3x/2x - 6

Plot Rational Function
Vertical Asymptote Horizontal Asymptote x-Intercept y-Intercept ​

Answer 1

Hello,

Explanation:

Vertical asymptote: x=3 because

`\displaystyle \lim_(n \to 3) (3x)/(2x-6) =\infty\\`

Horizontal asymptote: y=1.5 because

`\displaystyle \lim_(n \to \infty) (3x)/(2x-6) =(3)/(2) \\`

x-intercept: x=0

`if\ y=0 \ then \ (3x)/(2x-6) =0\Longrightarrow\ 3x=0\Longrightarrow\ x=0\\`

y-intercept: y=0

`if\ x=0\ then\ (3*0)/(2*0-6) =(0)/(-6)=0\\`