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