Use the graph below to find $\lim _ { x \rightarrow - 4 } \frac { | x + 4 | } { x + 4 }$, if it exists.

A) 1
B) $- 4$
C) 4
D) $- 1$
E) The limit does not exist.

Question

Use the graph below to find $\lim _ { x \rightarrow - 4 } \frac { | x + 4 | } { x + 4 }$, if it exists.

A) 1 
B) $- 4$ 
C) 4 
D) $- 1$ 
E) The limit does not exist.

Quizplus · Accepted Answer

As $x$ approaches $-4$ from the left, the expression $\frac{|x+4|}{x+4}$ approaches $-1$, while as $x$ approaches $-4$ from the right, the expression approaches $1$. Therefore, the limit does not exist.

Use the Graph Below to Find lim⁡x→−4∣x+4∣x+4\lim _ { x \rightarrow - 4 } \frac { | x + 4 | } { x + 4 }limx→−4​x+4∣x+4∣​

Use the Graph Below to Find $\lim _ { x \rightarrow - 4 } \frac { | x + 4 | } { x + 4 }$