The function [tex]$f(x)=\frac{-4}{x}+1$[/tex] has a vertical asymptote at:

A. [tex]$x=-1$[/tex]
B. [tex]$x=1$[/tex]
C. [tex]$f(x)=-1$[/tex]
D. [tex]$x=0$[/tex]



Answer :

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]