a third - degree polynomial function has three real zeros, has a relative minimum at (2,-3), and increases…

Explanation:

Step1: Analyze end - behavior

A third - degree polynomial with a positive leading coefficient has end - behavior of $y\to-\infty$ as $x\to-\infty$ and $y\to\infty$ as $x\to\infty$. Since the function increases on $(-\infty,-3)$, the leading coefficient is positive.

Step2: Mark key points

Mark the relative minimum point $(2, - 3)$ on the graph.

Step3: Consider zeros

Since it has three real zeros, and we know the behavior of the function. The function is increasing on $(-\infty,-3)$, then it must cross the x - axis at some point in $(-\infty,-3)$. After the relative minimum at $(2,-3)$, it will cross the x - axis again.

Step4: Sketch the curve

Start from the lower left (as $x\to-\infty,y\to-\infty$), increase until reaching a zero in $(-\infty,-3)$, then continue to increase until the relative minimum at $(2,-3)$, and then increase again towards the upper right (as $x\to\infty,y\to\infty$), crossing the x - axis two more times.

Answer:

Sketch a curve with the above - described features on the given coordinate grid. (Note: A detailed hand - drawn or digital sketch following the steps above should be made on the provided grid, showing an increasing part on $(-\infty,-3)$, a relative minimum at $(2,-3)$ and crossing the x - axis three times).