Determine whether f is continuous at c.
- $f ( x ) = \left\{ \begin{aligned}- 2 x + 3 , & x < 1 \\1 , & x = 1 ; \quad c = 1 \\4 x - 1 , & x > 1\end{aligned} \right.$

Question

Determine whether f is continuous at c.
-$$f ( x ) = \left\{ \begin{aligned}
- 2 x + 3 , & x < 1 \
1 , & x = 1 ; \quad c = 1 \
4 x - 1 , & x > 1
\end{aligned} \right.$$
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 limit as x approaches 1 from the left is -2(1) + 3 = 1, and from the right is 4(1) - 1 = 3. Since these limits are not equal, and also the limit from the right does not equal the function's value at x = 1 (which is 1), the function is not continuous at c = 1.

Determine Whether F Is Continuous at C f(x)={−2x+3,x<11,x=1;c=14x−1,x>1f ( x ) = \left\{ \begin{aligned}- 2 x + 3 , & x < 1 \\1 , & x = 1 ; \quad c = 1 \\4 x - 1 , & x > 1\end{aligned} \right.f(x)=⎩⎨⎧​−2x+3,1,4x−1,​x<1x=1;c=1x>1​

Determine Whether F Is Continuous at C $f ( x ) = \left\{ \begin{aligned}- 2 x + 3 , & x < 1 \\1 , & x = 1 ; \quad c = 1 \\4 x - 1 , & x > 1\end{aligned} \right.$