Question

let $f(x) = -dfrac{3}{x + 3}$.
a) enter the equation of the vertical asymptote of $f(x)$.

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, \( f(x)=-\frac{3}{x + 3} \), so \( h(x)=x + 3 \).

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

Set \( x + 3=0 \). Solving for \( x \), we get \( x=-3 \).
Check: When \( x = - 3 \), the numerator \( -3
eq0 \), so \( x=-3 \) is a vertical asymptote.

Answer:

\( x = - 3 \)