<h2>
Answer:</h2>
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.
<h2>
Step-by-step explanation:</h2>
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
