Question 4 of 12 , Step 1 of 1 Correct Find equations for the vertical asymptotes, if any, for the following rational function. \[ f(x)=\frac{-6 x^{2}+21 x-15}{-2 x-7} \] Answer

Step 1 ：The vertical asymptotes of a rational function occur at the values of x that make the denominator equal to zero, as long as they don't also make the numerator zero.

Step 2 ：So, we need to find the roots of the denominator, \(-2x - 7 = 0\), and check that they are not also roots of the numerator, \(-6x^2 + 21x - 15 = 0\).

Step 3 ：The roots of the denominator are \([-7/2]\).

Step 4 ：The roots of the numerator are \([1, 5/2]\).

Step 5 ：The asymptotes are \([-7/2]\).

Step 6 ：Final Answer: The vertical asymptote of the function is \(\boxed{x = \frac{7}{2}}\).