Question

1. consider the function $f(x) = \frac{4}{x} + 1$. 6a write the equation of the vertical asymptote. enter your next step here

Explanation:

Step1: Recall vertical asymptote rule

For a rational function \( f(x)=\frac{g(x)}{h(x)} \), vertical asymptotes occur where \( h(x) = 0 \) (and \( g(x)
eq0 \) at those points). Here, \( f(x)=\frac{4}{x}+1=\frac{4 + x}{x} \), so \( h(x)=x \).

Step2: Solve \( h(x)=0 \)

Set \( x = 0 \). Check \( g(x)=4 + x \) at \( x = 0 \): \( 4+0 = 4
eq0 \). So vertical asymptote is at \( x = 0 \).

Answer:

\( x = 0 \)