To find the value of [tex]\( x \)[/tex] where the function [tex]\( F(x) = \frac{3}{x+5} \)[/tex] has a vertical asymptote, we need to determine the value of [tex]\( x \)[/tex] that makes the denominator zero, as a vertical asymptote occurs where the function value tends to infinity, which happens when the denominator is zero in a rational function.
Let's set the denominator equal to zero:
[tex]\[
x + 5 = 0
\][/tex]
Next, we solve for [tex]\( x \)[/tex]:
[tex]\[
x = -5
\][/tex]
Thus, the value of [tex]\( x \)[/tex] where the function [tex]\( F(x) \)[/tex] has a vertical asymptote is [tex]\( -5 \)[/tex].
So, the correct answer is:
C. [tex]\(-5\)[/tex]
