$\text { Find the } x \text {-values (if any) at which } f ( x ) = \frac { | x - 3 | } { x - 3 } \text { is not continuous. }$
A) $f ( x )$ is not continuous at $x = 3$ and the discontinuity is nonremovable.
B) $f ( x )$ is not continuous at $x = 0$ and the discontinuity is removable.
C) $f ( x )$ is continuous for all real $x$.
D) $f ( x )$ is not continuous at $x = 3$ and the discontinuity is removable.
E) $f ( x )$ is not continuous at $x = 0 , - 3$ and $x = 0$ is a removable discontinuity.

Question

$\text { Find the } x \text {-values (if any) at which } f ( x ) = \frac { | x - 3 | } { x - 3 } \text { is not continuous. }$ 
A) $f ( x )$ is not continuous at $x = 3$ and the discontinuity is nonremovable.
B) $f ( x )$ is not continuous at $x = 0$ and the discontinuity is removable.
C) $f ( x )$ is continuous for all real $x$.
D) $f ( x )$ is not continuous at $x = 3$ and the discontinuity is removable.
E) $f ( x )$ is not continuous at $x = 0 , - 3$ and $x = 0$ is a removable discontinuity.

Quizplus · Accepted Answer

The function $f(x) = \frac{|x - 3|}{x - 3}$ is undefined at $x = 3$ because the denominator becomes zero, causing a division by zero. This results in a nonremovable discontinuity at $x = 3$.

Find the x-values (if any) at which f(x)=∣x−3∣x−3 is not continuous. \text { Find the } x \text {-values (if any) at which } f ( x ) = \frac { | x - 3 | } { x - 3 } \text { is not continuous. } Find the x-values (if any) at which f(x)=x−3∣x−3∣​ is not continuous.

$\text { Find the } x \text {-values (if any) at which } f ( x ) = \frac { | x - 3 | } { x - 3 } \text { is not continuous. }$