Find all points of discontinuity of the function. $$h ( x ) = \left\{ \begin{aligned} 4 - x & \text { if } x 4 \end{aligned} \right.$$ A) $x = 0 , x = 4$ B) $x = 0 , x = 4 , x = 8$ C) $x = 4$ D) $x = 0$ E) The function is continuous everywhere.

Question

Find all points of discontinuity of the function.   $$h ( x ) = \left\{ \begin{aligned}
4 - x & \text { if } x < 4 \
3 & \text { if } x = 4 \
x + 1 & \text { if } x > 4
\end{aligned} \right.$$  
A) $x = 0 , x = 4$
B)   $x = 0 , x = 4 , x = 8$
C)   $x = 4$
D)   $x = 0$
E)  The function is continuous everywhere.

Quizplus · Accepted Answer

The function is defined piecewise with different expressions for $x < 4$, $x = 4$, and $x > 4$. At $x = 4$, the function explicitly takes the value 3, which is different from the limit of $4 - x$ as $x$ approaches 4 from the left (which is 0) and the limit of $x + 1$ as $x$ approaches 4 from the right (which is 5). Therefore, the only point of discontinuity is at $x = 4$, where the function's value and the limits from either side do not match.

Find All Points of Discontinuity of the Function h(x)={4−x if x<43 if x=4x+1 if x>4h ( x ) = \left\{ \begin{aligned}4 - x & \text { if } x < 4 \\3 & \text { if } x = 4 \\x + 1 & \text { if } x > 4\end{aligned} \right.h(x)=⎩⎨⎧​4−x3x+1​ if x<4 if x=4 if x>4​

Find All Points of Discontinuity of the Function $h ( x ) = \left\{ \begin{aligned}4 - x & \text { if } x < 4 \\3 & \text { if } x = 4 \\x + 1 & \text { if } x > 4\end{aligned} \right.$