From the information provided in the function:
[tex]f(x)=\frac{-3x^2+7x+1}{x-2}[/tex]
We will have that there is an slanted asymptote [Since the degree of the denominator is less than the degree of the numerator by 1], now we determine the slanted asymptote:
We solve by using the synthetic division, that is:
| x^2 x^1 x^0
2 | -3 7 1
| -6 2
-------------------------------------
| -3 1 3
Thus the quotient is:
[tex]-3x+1[/tex]
And the remainder is 3.
From this, we have that the oblique asymptote follows the line:
[tex]y=-3x+1[/tex]
[Fourth option]
