Question

graph of $k(x)$

1. $lim_{x

ightarrow5^{-}}k(x)=$

1. $lim_{x

ightarrow3^{+}}k(x)=$

1. $lim_{x

ightarrow-infty}k(x)=$

1. $lim_{x

ightarrowinfty}k(x)=$

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:

1. \(-\infty\)
2. \(-\infty\)
3. \(0\)
4. \(0\)