Question

1. for what x-value(s) is the function shown below discontinuous?

$x=0$ and $x=1$
$x=-1$ and $x=1$
$x=1$
$x=0$ and $x=-1$

Explanation:

Step1: Identify discontinuity cues

A function is discontinuous at x-values where there are vertical asymptotes, holes, or breaks in the graph.

Step2: Locate vertical asymptotes

From the graph, vertical asymptotes exist at $x=0$ (the y-axis, where the graph shoots to ±∞) and $x=1$ (another vertical line where the graph has a break and shoots to ±∞).

Step3: Match to options

The x-values of discontinuity are $x=0$ and $x=1$, which matches the first option.

Answer:

x = 0 and x = 1