Video: Identifying the Degree of a Polynomial Function from its Graph

The given graph is of a polynomial 𝑓. What is the degree of 𝑓? [A] 1 [B] 2 [C] 3 [D] 4 [E] 5


Video Transcript

The given graph is of a polynomial 𝑓. What is the degree of 𝑓? Is it one, two, three, four, or five?

Remember, a polynomial of degree or order 𝑛 can have up to 𝑛 minus one turning points. In other words, if we can find the degree of our polynomial, we can know it can have up to one less than this turning points. So, let’s count the turning points of our graph. We see the graph changes direction here and here. But what’s happening over here? Well, the graph doesn’t actually appear to fully change direction, and that’s because it doesn’t. This is, in fact, a point of inflection. It’s a point where the concavity of the graph changes.

Now, another fact is that a polynomial of degree 𝑛 can have up to 𝑛 minus two inflection points. And we can think of the inflection points a little bit like the graph changing direction really quickly twice in a short space of time. We can consider this as two turning points. This means we have a total of four. And so, the degree of our polynomial must be five.

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