Question

ving end behaviors. b) $lim_{x
ightarrow-infty}g(x)=-infty$ $lim_{x
ightarrowinfty}g(x)=+infty$

Explanation:

Step1: Analyze the left - hand limit

As \(x\to-\infty\), the limit \(\lim_{x\to-\infty}g(x)=-\infty\) means that as \(x\) takes on increasingly large negative values, the function \(g(x)\) decreases without bound. This is consistent with the left - hand side of the graph where the curve is going downwards as we move to the left.

Step2: Analyze the right - hand limit

As \(x\to\infty\), the limit \(\lim_{x\to\infty}g(x)=+\infty\) means that as \(x\) takes on increasingly large positive values, the function \(g(x)\) increases without bound. This is consistent with the right - hand side of the graph where the curve is going upwards as we move to the right.

Answer:

The given end - behaviors \(\lim_{x\to-\infty}g(x)=-\infty\) and \(\lim_{x\to\infty}g(x)=+\infty\) match the graph shown.