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 a function to be continuous at a point c, the limit as x approaches c from the left must equal the limit as x approaches c from the right, and both must equal the function's value at c. Here, the left-hand limit as x approaches 1 is $-2(1) + 9 = 7$, and the right-hand limit as x approaches 1 is $-7(1) + 14 = 7$. However, the function is not defined at $x = 1$, making it discontinuous 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 $f ( x ) = \left\{ \begin{array} { r l } - 2 x + 9 , & x < 1 \\- 7 x + 14 , & x > 1\end{array} ; \quad c = 1 \right.$