Find the numbers at which f is continuous. At which numbers is f discontinuous? -$$f ( x ) = \left\{ \begin{aligned} 7 x & \text { if } x 6 \end{aligned} \right.$$ A) continuous for all real numbers B) continuous for all real numbers except $x = 7 , x = 6$ C) continuous for all real numbers except $x = 6$ D) continuous for all real numbers except $x = 0 , x = 6$

Question

Find the numbers at which f is continuous. At which numbers is f discontinuous?
-$$f ( x ) = \left\{ \begin{aligned}
7 x & \text { if } x < 6 \
41 & \text { if } x = 6 \
x ^ { 2 } + 6 & \text { if } x > 6
\end{aligned} \right.$$
A) continuous for all real numbers
B) continuous for all real numbers except $x = 7 , x = 6$
C) continuous for all real numbers except $x = 6$
D) continuous for all real numbers except $x = 0 , x = 6$

Quizplus · Accepted Answer

The function is continuous for all real numbers except at $x = 6$, where there is a jump discontinuity. For $x < 6$, the function is defined as $7x$, and for $x > 6$, it is defined as $x^2 + 6$. At $x = 6$, the function takes a specific value of 41, which does not match the limit of $7x$ or $x^2 + 6$ as $x$ approaches 6 from either side.

Find the Numbers at Which F Is Continuous f(x)={7x if x<641 if x=6x2+6 if x>6f ( x ) = \left\{ \begin{aligned}7 x & \text { if } x < 6 \\41 & \text { if } x = 6 \\x ^ { 2 } + 6 & \text { if } x > 6\end{aligned} \right.f(x)=⎩⎨⎧​7x41x2+6​ if x<6 if x=6 if x>6​

Find the Numbers at Which F Is Continuous $f ( x ) = \left\{ \begin{aligned}7 x & \text { if } x < 6 \\41 & \text { if } x = 6 \\x ^ { 2 } + 6 & \text { if } x > 6\end{aligned} \right.$