which statement is true about the function y = x / (x² - x)? select one: a. it has a point of discontinuity…

Explanation:

Step1: Simplify the function

First, factor the denominator: $y=\frac{x}{x(x - 1)}=\frac{1}{x - 1},x\neq0$.

Step2: Analyze point of discontinuity

The original function $y=\frac{x}{x^{2}-x}$ is undefined at $x = 0$ and $x=1$. After simplification, the removable - discontinuity is at $x = 0$. When $x = 0$, the simplified function $y=\frac{1}{x - 1}=-1$. So, there is a point of discontinuity at $(0,-1)$.

Step3: Analyze vertical asymptote

The vertical asymptote of $y=\frac{1}{x - 1}$ is $x = 1$, not $x = 0$.

Step4: Analyze x - intercept

Set $y = 0$, then $\frac{1}{x - 1}=0$. There is no solution for this equation, so there is no x - intercept.

Step5: Analyze y - intercept

The function is undefined at $x = 0$, so there is no y - intercept.

Answer:

A. It has a point of discontinuity at $(0,-1)$