Question

use the following function and its graph to answer parts a through d below. let ( f(x) = \begin{cases} 5 - x, & x < 3 \\ 3, & x = 3 \\ dfrac{2x}{3}, & x > 3 end{cases} ) find ( limlimits_{x \to 3^-} f(x) ). select the correct choice below and, if necessary, fill in the answer box in your choice. a. ( limlimits_{x \to 3^-} f(x) = 2 ) (simplify your answer.) b. the limit does not exist. find ( f(3) ). select the correct choice below and, if necessary, fill in the answer box in your choice. a. ( f(3) = square ) (simplify your answer.) b. ( f(3) ) does not exist.

Explanation:

For finding \( f(3) \):

Step1: Identify the piece for \( x = 3 \)

The function \( f(x) \) is defined as \( f(x)=3 \) when \( x = 3 \) (from the piecewise function: \(

$$\begin{cases} 5 - x, & x < 3 \\ 3, & x = 3 \\ \frac{2x}{3}, & x > 3 \end{cases}$$

\)).

Step2: Determine \( f(3) \)

Since for \( x = 3 \), the function value is given as 3, we have \( f(3)=3 \).

Answer:

A. \( f(3)=\boldsymbol{3} \) (Simplify your answer.)