Find the numbers at which f is continuous. At which numbers is f discontinuous?
-$$f ( x ) = \left\{ \begin{aligned}
x - 5 & \text { if } x \leq 5 \
2 x - 10 & \text { if } x 5
\end{aligned} \right.$$
A) continuous for all real numbers except $x = - 5 , x = 5$
B) continuous for all real numbers except $x = 5$
C) continuous for all real numbers
D) continuous for all real numbers except $x = 0$

Question

Find the numbers at which f is continuous. At which numbers is f discontinuous?
-$$f ( x ) = \left\{ \begin{aligned}
x - 5 & \text { if } x \leq 5 \
2 x - 10 & \text { if } x > 5
\end{aligned} \right.$$
A) continuous for all real numbers except $x = - 5 , x = 5$
B) continuous for all real numbers except $x = 5$
C) continuous for all real numbers
D) continuous for all real numbers except $x = 0$

Quizplus · Accepted Answer

The function is continuous for all real numbers because at $x = 5$, both pieces of the piecewise function equal the same value, $0$. For $x \leq 5$, $f(x) = x - 5$, and for $x > 5$, $f(x) = 2x - 10$. At $x = 5$, both expressions equal $0$, ensuring continuity at $x = 5$, and elsewhere the function is defined and continuous.

Find the Numbers at Which F Is Continuous f(x)={x−5 if x≤52x−10 if x>5f ( x ) = \left\{ \begin{aligned}x - 5 & \text { if } x \leq 5 \\2 x - 10 & \text { if } x > 5\end{aligned} \right.f(x)={x−52x−10​ if x≤5 if x>5​

Find the Numbers at Which F Is Continuous $f ( x ) = \left\{ \begin{aligned}x - 5 & \text { if } x \leq 5 \\2 x - 10 & \text { if } x > 5\end{aligned} \right.$