Find the numbers, if any, where the function $f ( x ) = \left\{ \begin{array} { c c } 3 x - 2 & \text { if } x \leq 1 \ 0 & \text { if } x 1 \end{array} \right.$ is discontinuous.
A) $- 2$
B) 2
C) 1
D) 0

Question

Find the numbers, if any, where the function $f ( x ) = \left\{ \begin{array} { c c } 3 x - 2 & \text { if } x \leq 1 \ 0 & \text { if } x > 1 \end{array} \right.$ is discontinuous.
A) $- 2$
B) 2
C) 1
D) 0

Quizplus · Accepted Answer

The function $f(x)$ is discontinuous at $x = 1$ because the definition of the function changes at that point, and there is a jump discontinuity. For $x \leq 1$, the function is defined as $3x - 2$, and for $x > 1$, the function is defined as $0$. This change in definition at $x = 1$ causes the discontinuity.

Find the Numbers, If Any, Where the Function f(x)={3x−2 if x≤10 if x>1f ( x ) = \left\{ \begin{array} { c c } 3 x - 2 & \text { if } x \leq 1 \\ 0 & \text { if } x > 1 \end{array} \right.f(x)={3x−20​ if x≤1 if x>1​

Find the Numbers, If Any, Where the Function $f ( x ) = \left\{ \begin{array} { c c } 3 x - 2 & \text { if } x \leq 1 \\ 0 & \text { if } x > 1 \end{array} \right.$