Question

How do you graph `y=(9x+1)/(3x-2)` using asymptotes, intercepts, end behavior?

Answer 1

Horizontal Asymptote :`y=3`
Vertical Asymptote: `x=2/3`

Explanation:

You can Horizontal asymptote by making denominator of the rational function to zero
`3x-2=0`
`x=2/3`

You can find Vertical asymptote by finding the ratio of leading coefficient in the numerator to leading coefficient of the denominator
`y=9/3=3`

Y-intercept can be found by making `x=0`
`(0,-1/2)`

X-intercept can be found by making numerator =0
`9x+1=0`
`x=-1/9`
`(-1/9,0)`

graph{y=(9x+1)/(3x-2) [-8.36, 11.64, -3.12, 6.88]}