Find all the discontinuities of $f ( x ) = \left\{ \begin{array} { c c }
x ^ { 2 } & \text { if } x \leq 3 \
9 & \text { if } 3

Question

Find all the discontinuities of $f ( x ) = \left\{ \begin{array} { c c } 
x ^ { 2 } & \text { if } x \leq 3 \
9 & \text { if } 3 < x < 5 \
2 x + 1 & \text { if } x \geq 5
\end{array} \right.$
A) 5 and 9
B) 5
C) 9
D) f is continuous everywhere.

Quizplus · Accepted Answer

The function $f(x)$ is discontinuous at $x = 5$ because the value of the function jumps from 9 to 11 (since $2(5) + 1 = 11$) at that point. At $x = 3$, the function is continuous because the value from both sides is $3^2 = 9$. There is no discontinuity at $x = 9$ since it is not a point where the definition of the function changes.

Find All the Discontinuities Of A) 5 and 9 B) 5 C) 9 D) F

Find All the Discontinuities Of A) 5 and 9
B) 5
C) 9
D) F