`f(x)=(6x-1)/(3x-1)` Graph the function. State the domain and range.

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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.

The graph:

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