graph of $k(x)$\n13. $lim_{x\rightarrow5^{-}}k(x)=$\n14. $lim_{x\rightarrow3^{+}}k(x)=$\n15…

Explanation:

Step1: Analyze left - hand limit as x approaches 5

As (x) approaches (5) from the left ((x\to5^{-})), we look at the behavior of the graph of (y = k(x)) for values of (x) that are less than (5) but getting closer to (5). From the graph, as (x) approaches (5) from the left, (k(x)\to-\infty).

Step2: Analyze right - hand limit as x approaches 3

As (x) approaches (3) from the right ((x\to3^{+})), we look at the behavior of the graph of (y = k(x)) for values of (x) that are greater than (3) but getting closer to (3). From the graph, as (x) approaches (3) from the right, (k(x)\to-\infty).

Step3: Analyze limit as x approaches negative infinity

As (x\to-\infty), we observe the long - term behavior of the graph as (x) takes on increasingly large negative values. The graph of (k(x)) approaches (0) as (x\to-\infty).

Step4: Analyze limit as x approaches positive infinity

As (x\to\infty), we observe the long - term behavior of the graph as (x) takes on increasingly large positive values. The graph of (k(x)) approaches (0) as (x\to\infty).

Answer:

13. (-\infty)
14. (-\infty)
15. (0)
16. (0)