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. Select the correct answer.
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. Select the correct answer.
A) $- 2$
B) 2
C) 1
D) 0

Quizplus · Accepted Answer

The function is continuous for $x>1$ since it is just constant $0$. Therefore, the potential discontinuity must occur at $x=1$. Checking from the left and right, we see that $\lim_{x	o 1^-}f(x)=3(1)-2=1$ and $\lim_{x	o 1^+}f(x)=0$. Since these limits are not equal, the function is discontinuous at $x=1$.

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 $f ( x ) = \left\{ \begin{array} { c c } 3 x - 2 & \text { if } x \leq 1 \\ 0 & \text { if } x > 1 \end{array} \right.$