12) \( f(\mathrm{x})=\frac{4}{x-4} \) Find the vertical asymptote(s). \( \mathrm{x}=0 \) \( \mathrm{x}=4 \) \( \mathrm{x}=-4,4 \)

To find the vertical asymptote of the function \( f(x) = \frac{4}{x-4} \), we want to determine where the function is undefined, which occurs when the denominator is zero. Setting the denominator equal to zero gives us \( x - 4 = 0 \), leading to \( x = 4 \). Hence, the vertical asymptote is at \( x = 4 \). A common mistake when finding vertical asymptotes is including values that don’t actually make the denominator zero. In this case, options such as \( x = 0 \) or \( x = -4 \) are incorrect because they do not lead to undefined points in the function. Always check where the denominator equals zero to pinpoint vertical asymptotes accurately!