Let $f ( x ) = \frac { | x | } { 5 x }$ Which of the following is true?

A)ƒ is defined at 0.
B)ƒ is discontinuous at -1.
C)ƒ has a removable discontinuity at 0.
D)ƒ has a removable discontinuity at -1.
E)ƒ has a jump discontinuity at 0.

Question

Let $f ( x ) = \frac { | x | } { 5 x }$ Which of the following is true?

A)ƒ is defined at 0.
B)ƒ is discontinuous at -1.
C)ƒ has a removable discontinuity at 0.
D)ƒ has a removable discontinuity at -1.
E)ƒ has a jump discontinuity at 0.

Quizplus · Accepted Answer

The function $f(x) = \frac{|x|}{5x}$ is not defined at $x = 0$ because the denominator becomes 0, leading to a division by zero. For $x > 0$, $f(x) = \frac{x}{5x} = \frac{1}{5}$, and for $x < 0$, $f(x) = \frac{-x}{5x} = -\frac{1}{5}$. This means the function jumps from $\frac{1}{5}$ to $-\frac{1}{5}$ as $x$ crosses 0, indicating a jump discontinuity at $x = 0$.

Let f(x)=∣x∣5xf ( x ) = \frac { | x | } { 5 x }f(x)=5x∣x∣​

Let $f ( x ) = \frac { | x | } { 5 x }$