4. Polynomial Functions

Graphing Polynomial Functions

4. Polynomial Functions

Graphing Polynomial Functions

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Multiple Choice

Based on the known points plotted on the graph, determine what intervals the graph should be broken into.
Plotted points are: $\left(-3,0\right),$ $\left(0,1\right),\left(2,0\right),$ & $\left(5,0\right)$

$-\infty\rightarrow-3,-3\rightarrow0,0\rightarrow5,5\rightarrow\infty$

$-\infty\rightarrow-3,-3\rightarrow0,0\rightarrow2,2\rightarrow5,5\rightarrow\infty$

$-\infty\rightarrow-3,-3\rightarrow0,0\rightarrow2,2\rightarrow\infty$

$-\infty\rightarrow0,0\rightarrow2,2\rightarrow5,5\rightarrow\infty$

Verified step by step guidance

Identify the plotted points on the graph: (-3,0), (0,1), (2,0), and (5,0). These points are crucial for determining the intervals.

Recognize that the x-values of these points are where the graph changes behavior or crosses the x-axis. These x-values are -3, 0, 2, and 5.

Determine the intervals based on these x-values. The graph should be broken into intervals where each segment represents a distinct behavior of the function.

The intervals are: (-∞, -3), (-3, 0), (0, 2), (2, 5), and (5, ∞). These intervals are chosen because they include all the critical x-values where the graph changes.

Verify that these intervals match the correct answer provided: (-∞, -3), (-3, 0), (0, 2), (2, 5), and (5, ∞). This confirms the intervals are correctly identified based on the plotted points.