What are the equations of the asymptotes of the graph of the function f(x)=3x^2-2x-1/x^2+3x-10

Vertical asymptotes x = 2, 5

Horizontal asymptotes y = 3

No oblique asymtotes.

Step-by-step explanation:

The given function is f(x) = (3x²-2x-1)/(x²+3x-10)

We have to write the equations of the asymptotes of the graph of the function given.

Now we will factorize the denominator

Denominator is (x² + 3x -10) = x² + 5x - 2x -10 = x(x-5)-2(x-5) = (x-2)(x-5)

So the function is f(x) = (3x² -2x -1)/(x-2)(x-5)

So the vertical asymptotes are x = 2, 5

Horizontal asymptote is y = 3 ( Quotient of the function when we divide numerator by the denominator of the function)

No Oblique asymptotes.