​The degree and leading coefficient of a function can tell us about multiple features of its graph.

Even degree polynomials have ends that either both go up or both go down.

Odd degree polynomials have ends that go in opposite directions.

A graph faces up on the right if it has a positive leading coefficient.

A graph faces down on the right if it has a negative leading coefficient.

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The function in the graph has an even degree and positive leading coefficient. We know this because both ends of the graph are going up forever.

End behavior in words:
As x is approaching negative infinity, y is approaching positive infinity. As x is approaching positive infinity, y is approaching positive infinity.

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The point where a graph switches from increasing to decreasing is called a local, or relative, maximum.



The point where a graph switches from decreasing to increasing is called a local, or relative, minimum.

The function f(x) has a local, or relative, minimum at (1.732, -6.392).

The function f(x) has a local, or relative, maximum at (-1.732, 14.392).

There are no absolute, or global, extrema in this graph.

The point (0, 5) is considered an absolute, or global, minimum.


This is because 5 is the smallest output value of the entire function.

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