To determine the vertical asymptote of the function \( f(x) = \frac{-4}{x} + 1 \), we need to focus on the part that makes the function undefined. In general, vertical asymptotes occur where the denominator of a fraction is zero, as the function tends to approach infinity or negative infinity there.
Let's examine the denominator of the fraction:
[tex]\[ f(x) = \frac{-4}{x} + 1 \][/tex]
The value of \( x \) that makes the denominator zero is:
[tex]\[ x = 0 \][/tex]
When \( x = 0 \), the denominator becomes zero, hence the function \( f(x) \) is undefined. Therefore, the vertical asymptote is at the value of \( x \) where \( x = 0 \).
Thus, the vertical asymptote of the function \( f(x) = \frac{-4}{x} + 1 \) is at:
[tex]\[ \boxed{x = 0} \][/tex]
So, the correct answer is:
D. [tex]\( x = 0 \)[/tex]
