Determine the limit by sketching an appropriate graph.
-$\lim _ { x \rightarrow 4 ^ { + } } f ( x ) \text {, where } f ( x ) = \left\{ \begin{array} { l l }
- 3 x - 5 & \text { for } x

Question

Determine the limit by sketching an appropriate graph.
-$\lim _ { x \rightarrow 4 ^ { + } } f ( x ) \text {, where } f ( x ) = \left\{ \begin{array} { l l } 
- 3 x - 5 & \text { for } x < 4 \
5 x - 4 & \text { for } x \geq 4
\end{array} \right.$

A) -4 
B) -3 
C) 16 
D) -17

Quizplus · Accepted Answer

To determine the limit as $x$ approaches $4^+$, we need to consider the right-hand side of the function: $5x-4$ for $x\ge4$. As $x$ approaches $4$ from the right, the function values approach $5(4)-4=16$. This can be seen in the graph by noticing that the function is continuous at $x=4$, and the value of the function at $x=4$ is $5(4)-4=16$. Therefore, the limit as $x$ approaches $4^+$ is 16, so the answer is C.

Determine the Limit by Sketching an Appropriate Graph A) -4 B) -3 C) 16 D) -17

Determine the Limit by Sketching an Appropriate Graph A) -4
B) -3
C) 16
D) -17