To determine the value of [tex]\( x \)[/tex] at which the graph of the function [tex]\( F(x) \)[/tex] has a vertical asymptote, we need to understand the conditions under which vertical asymptotes occur for rational functions.
A vertical asymptote occurs when the denominator of the rational function equals zero, provided that this does not also make the numerator zero (since this would potentially make the function undefined rather than creating an asymptote).
Given the function:
[tex]\[
F(x) = \frac{7x}{2x - 8}
\][/tex]
we focus on the denominator:
[tex]\[
2x - 8
\][/tex]
To find the vertical asymptote(s), we set the denominator equal to zero and solve for [tex]\( x \)[/tex]:
[tex]\[
2x - 8 = 0
\][/tex]
Adding 8 to both sides gives:
[tex]\[
2x = 8
\][/tex]
Dividing both sides by 2 yields:
[tex]\[
x = 4
\][/tex]
Thus, the function has a vertical asymptote at [tex]\( x = 4 \)[/tex].
So, the correct answer is:
C. 4
