Question

f(x)=\frac{1}{-4x + 12}
vertical asymptotes:
horizontal asymptotes:
holes:

Explanation:

Step1: Find vertical asymptote

Set denominator equal to zero: $-4x + 12=0$. Solve for $x$: $-4x=-12$, so $x = 3$.

Step2: Find horizontal asymptote

Degree of numerator ($0$) < degree of denominator ($1$). By rule, $y = 0$.

Step3: Check for holes

Factor numerator ($1$) and denominator ($-4(x - 3)$). No common factors. So no holes.

Answer:

Vertical Asymptotes: $x = 3$
Horizontal Asymptotes: $y = 0$
Holes: None