To determine where the graph of the function [tex]\( F(x) = \frac{2}{x-2} \)[/tex] has a vertical asymptote, we need to identify the points where the denominator of the function is zero but the numerator is not zero. Vertical asymptotes occur at these points because the function becomes undefined as it approaches these values on the x-axis.
Let’s follow these steps:
1. Identify the denominator:
The denominator in the given function [tex]\( F(x) = \frac{2}{x-2} \)[/tex] is [tex]\( x - 2 \)[/tex].
2. Set the denominator equal to zero:
To find the vertical asymptote, set [tex]\( x - 2 = 0 \)[/tex].
3. Solve for [tex]\( x \)[/tex]:
Solving this equation:
[tex]\[
x - 2 = 0
\][/tex]
[tex]\[
x = 2
\][/tex]
Therefore, the graph of the function [tex]\( F(x) = \frac{2}{x-2} \)[/tex] has a vertical asymptote at [tex]\( x = 2 \)[/tex].
The correct answer is:
C. [tex]\( 2 \)[/tex]
