Use the grid to graph the function. Find the limit, if it exists
-$$\lim _ { x \rightarrow 0 } f ( x ) , \quad f ( x ) = \left\{ \begin{array} { r l }
x + 1 & x

Question

Use the grid to graph the function. Find the limit, if it exists
-$$\lim _ { x \rightarrow 0 } f ( x ) , \quad f ( x ) = \left\{ \begin{array} { r l } 
x + 1 & x < 0 \
4 x + 1 & x \geq 0
\end{array} \right.$$
A) 0
B) 1
C) 5
D) does not exist

Quizplus · Accepted Answer

The limit as $x$ approaches 0 from the left side (for $x < 0$) is $0 + 1 = 1$, and from the right side (for $x \geq 0$) is $4(0) + 1 = 1$. Since both one-sided limits are equal to 1, the limit of $f(x)$ as $x$ approaches 0 exists and is equal to 1.

Use the Grid to Graph the Function lim⁡x→0f(x),f(x)={x+1x<04x+1x≥0\lim _ { x \rightarrow 0 } f ( x ) , \quad f ( x ) = \left\{ \begin{array} { r l } x + 1 & x < 0 \\4 x + 1 & x \geq 0\end{array} \right.x→0lim​f(x),f(x)={x+14x+1​x<0x≥0​

Use the Grid to Graph the Function $\lim _ { x \rightarrow 0 } f ( x ) , \quad f ( x ) = \left\{ \begin{array} { r l } x + 1 & x < 0 \\4 x + 1 & x \geq 0\end{array} \right.$