Problem
Give the equations of any vertical, horizontal, or oblique asymptotes for the graph of the rational function. State the domain of $\mathrm{f}$. \[ f(x)=\frac{3-2 x}{4 x+2} \] Identify any vertical asymptotes. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. There is one vertical asymptote. Its equation is $\square$. (Type an equation. Use integers or fractions for any numbers in the equation.) B. There are two vertical asymptotes. The equation of the leftmost one is $\square$ and the equation of the rightmost one is $\square$. (Type equations. Use integers or fractions for any numbers in the equations.) c. There areno vertical asymptotes.
Solution
Step 1 ：The vertical asymptotes of a rational function occur where the denominator is equal to zero and the numerator is not equal to zero. So, we need to solve the equation \(4x + 2 = 0\).
Step 2 ：Solving the equation \(4x + 2 = 0\), we get \(x = -\frac{1}{2}\).
Step 3 ：Therefore, there is one vertical asymptote at \(x = -\frac{1}{2}\).
Step 4 ：Final Answer: \(\boxed{x = -\frac{1}{2}}\)
