Question

Which statements are true about the graphs of all nth degree polynomials?

Answer 1

The statements are true about the graphs of all nth degree polynomials are B and D.

B. It goes up and down at most a total of n times.

D. The number of x-intercepts is at most n.

Answer 2

Answer:

The statement that is true about the graphs of all nth degree polynomials is:

B.) It goes up and down at most a total of n times.

D.) The number of x-intercepts is at most n.

Step-by-step explanation:

We know that the number of times the graph goes up and down depends on the number of distinct zeros of a polynomial and as we know that a polynomial of nth degree may have repetitive zero.

Hence, the graph of nth degree polynomial  goes up and down at most a total of n times.

Also, the number of x-intercept is the x-value of the point where the function is zero i.e. it depends on the number of zeros of polynomial.

Hence,  The number of x-intercepts is at most n.

Also, the end behavior of graph depends on degree as well as sign of the leading coefficient.

       Hence, correct options are:

      Option B and option: D