To determine the value of \( x \) at which the graph of the function \( F(x) = \frac{5x}{2x-6} \) has a vertical asymptote, we need to find the value of \( x \) that makes the denominator equal to zero, since division by zero is undefined and causes a vertical asymptote.
Let's analyze the denominator \( 2x - 6 \):
1. Set the denominator equal to zero:
[tex]\[
2x - 6 = 0
\][/tex]
2. Solve for \( x \):
[tex]\[
2x - 6 = 0
\][/tex]
Add 6 to both sides:
[tex]\[
2x = 6
\][/tex]
Divide both sides by 2:
[tex]\[
x = 3
\][/tex]
Thus, the function \( F(x) = \frac{5x}{2x-6} \) has a vertical asymptote at \( x = 3 \). This occurs because at \( x = 3 \), the denominator becomes zero, leading to an undefined value for \( F(x) \).
Therefore, the correct answer is:
A. 3
