Determine whether f is continuous at c.
- $f ( x ) = \left\{ \begin{array} { r l } - 2 x + 9 , & x < 1 \\- 7 x + 14 , & x > 1\end{array} ; \quad c = 1 \right.$

Question

Determine whether f is continuous at c.
-$$f ( x ) = \left\{ \begin{array} { r l } 
- 2 x + 9 , & x < 1 \
- 7 x + 14 , & x > 1
\end{array} ; \quad c = 1 \right.$$
A) not continuous
B) continuous

Quizplus · Accepted Answer

For continuity at $c = 1$, the limit of $f(x)$ as $x$ approaches 1 from both sides must exist and be equal to $f(1)$. However, $f(x)$ is not defined at $x = 1$, and the limits from the left and right do not match. Therefore, $f$ is not continuous at $c = 1$.

Determine Whether F Is Continuous at C f(x)={−2x+9,x<1−7x+14,x>1;c=1f ( x ) = \left\{ \begin{array} { r l } - 2 x + 9 , & x < 1 \\- 7 x + 14 , & x > 1\end{array} ; \quad c = 1 \right.f(x)={−2x+9,−7x+14,​x<1x>1​;c=1

Determine Whether F Is Continuous at C $f ( x ) = \left\{ \begin{array} { r l } - 2 x + 9 , & x < 1 \\- 7 x + 14 , & x > 1\end{array} ; \quad c = 1 \right.$