Question

use the following function and its graph to answer parts a through d below.
let ( f(x) = \begin{cases} 8 - x, & x < 6 \\ 3, & x = 6 \\ \frac{x}{3}, & x > 6 end{cases} )

find ( limlimits_{x \to 6^-} f(x) ). select the correct choice below and, if necessary, fill in the answer box in your choice.
a. ( limlimits_{x \to 6^-} f(x) = 2 ) (simplify your answer.)
b. the limit does not exist.

find ( f(6) ). select the correct choice below and, if necessary, fill in the answer box in your choice.
a. ( f(6) = square ) (simplify your answer.)
b. ( f(6) ) does not exist.

Explanation:

For $\boldsymbol{\lim_{x \to 6^-} f(x)}$:

Step1: Identify the relevant piece

For $x < 6$, the function is $f(x) = 8 - x$.

Step2: Substitute the limit value

As $x \to 6^-$, we substitute $x = 6$ into $8 - x$: $8 - 6 = 2$.

Step1: Identify the relevant piece

For $x = 6$, the function is defined as $f(x) = 3$.

Step2: Get the value

So $f(6) = 3$.

Answer:

$\lim_{x \to 6^-} f(x) = 2$

For $\boldsymbol{f(6)}$: