Question

Which is a graph of f(x) = (6x-2)/(x-3), with any vertical or horizontal asymptotes indicated by the dashed lines?

Answer 1

to find the vertical asymptote, you have to put the rational function in the simplest form, which means to cancel any common factor between the numerator and denominator. here we don't have anything to cancel. then take the denominator and equal it to 0. x-3=0 ,x=3

to find the horizontal asymptote, in this situation, the degree of the numerator and denominator are the same which is 1. therefore, y=the coefficient of the numerator ÷ the coefficient of the denominator. y=6÷1 ,y=6

Answer 2

Answer with explanation:

The given function is:

`f(x)=(6x-2)/(x-3)`

Horizontal Asymptote

`y= \lim_(x \to \infty) (6x-2)/(x-3)\\\\\text{Dividing Numerator and Denominator by ,x}\\\\\Rightarrow y=\lim_(x \to \infty) (6-(2)/(x))/(1-(3)/(x))\\\\\Rightarrow y=(6-0)/(1-0)\\\\\Rightarrow y=6`

Vertical Asymptote

→Substitute Denominator of f(x) =0

⇒x-3=0

⇒x=3

⇒x=3 is Vertical Asymptote , and y=6 is horizontal Asymptote.

Matching with all the options

Option D