`f(x)=(6x-1)/(3x-1)` Graph the function. State the domain and range.
We are asked to graph the function `y=(6x-1)/(3x-1) ` :
The graph has a vertical asymptote at x=1/3. The graph has a horizontal asymptote at y=2.
Thus the domain is all reals except 1/3 and the range is all reals except 2.
Using division we can rewrite the function as ` y=1/(3(x-1/3))+2` ; using y=1/x as the base graph the transformation has been shifted right 1/3 units and up 2 units with a vertical dilation of factor 3.