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Sketching Polynomial Functions

Sketching Polynomial Functions 1.19 - Solution

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a

End behavior is the behavior of the graph of as approaches positive or negative infinity. Let's consider the given graph.

We can see above that as approaches negative infinity, approaches negative infinity. As approaches positive infinity, approaches negative infinity.

b
From Part A, we know that the end behavior goes in the same direction on both ends. This means that the graph crosses the axis an even number of times, in this case that number is Therefore, the given graph represents an even-degree function.
End Behavior Type of Function
Same Direction Even-degree function
Opposite Directions Odd-degree function