Answer :
To determine the value of [tex]\( x \)[/tex] at which the function [tex]\( F(x) = \frac{3}{x+5} \)[/tex] has a vertical asymptote, you need to find where the denominator of the function is equal to zero, as this will make the function undefined and create a vertical asymptote. Let's work through the problem step-by-step:
1. Identify the denominator of the function [tex]\( F(x) \)[/tex]:
[tex]\[ \text{Denominator} = x + 5 \][/tex]
2. Set the denominator equal to zero and solve for [tex]\( x \)[/tex]:
[tex]\[ x + 5 = 0 \][/tex]
3. Solve the equation:
[tex]\[ x = -5 \][/tex]
Therefore, the vertical asymptote occurs at [tex]\( x = -5 \)[/tex].
Hence, the correct answer is:
A. -5
1. Identify the denominator of the function [tex]\( F(x) \)[/tex]:
[tex]\[ \text{Denominator} = x + 5 \][/tex]
2. Set the denominator equal to zero and solve for [tex]\( x \)[/tex]:
[tex]\[ x + 5 = 0 \][/tex]
3. Solve the equation:
[tex]\[ x = -5 \][/tex]
Therefore, the vertical asymptote occurs at [tex]\( x = -5 \)[/tex].
Hence, the correct answer is:
A. -5
