Question

Could the equation. For the graph of the function have degree 4?explain

Answer 1

The graphed polynomial seems to have a degree of 2, so the degree can be 4 and not 5.

Could the graphed function have a degree 4?

For a polynomial of degree N, we have (N - 1) changes of curvature.

This means that a quadratic function (degree 2) has only one change (like in the graph).

Then for a cubic function (degree 3) there are two, and so on.

So. a polynomial of degree 4 should have 3 changes. Naturally, if the coefficients of the powers 4 and 3 are really small, the function will behave like a quadratic for smaller values of x, but for larger values of x the terms of higher power will affect more, while here we only see that as x grows, the arms of the graph only go upwards (we don't know what happens after).

Then we can write:

y = a*x^4 + c*x^2 + d

That is a polynomial of degree 4, but if we choose x^2 = u

y = a*u^2 + c*u + d

So it is equivalent to a quadratic polynomial.

Then the graph can represent a function of degree 4 (but not 5, as we can't perform the same trick with an odd power).

If you want to learn more about polynomials:

brainly.com/question/4142886

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