Question

which graph description best matches:$f(x) = \frac{x-1}{x^3}$○ a vertical asymptote at $x = 0$ and an x-intercept at $x = 1$○ two vertical asymptotes at $x = \pm1$○ a hole at $x = 0$○ one vertical asymptote at $x = 1$

Explanation:

Step1: Find undefined x-values

Set denominator to 0: $x^3 = 0 \implies x=0$

Step2: Check for common factors

Numerator $x-1$ and denominator $x^3$ share no common factors.

Step3: Find x-intercept

Set numerator to 0: $x-1=0 \implies x=1$

Answer:

A. A vertical asymptote at $x = 0$ and an x-intercept at $x = 1$