What are the characteristics of the function f(x) = 2(x - 4)5?A.It has 4 zeros and at most 5 relative maximums or minimums.B.It has 5 zeros and at most 4 relative maximums or minimums.C.It is a vertical stretch and a translation to the right of the parent function.D.The left end of the graph of the function goes down, and the right end goes up.E.Both ends of the graph of the function go up.F.It is a reflection and a translation to the right of the parent function.SUBMITarrow_backPREVIOUS

The function f(x) = 2(x - 4)5 is a polynomial function of degree 5. Here are the characteristics of this function:

A. It has 1 zero, not 4. The zero of this function is x = 4.

B. It does not have 5 zeros. Polynomial functions have as many zeros as their degree, counting multiplicity. Since the degree of this function is 5, it could have up to 5 zeros, but in this case, it only has 1 zero at x = 4.

C. This statement is correct. The function is a vertical stretch by a factor of 2 and a translation 4 units to the right of the parent function y = x5.

D. This statement is correct. Since the degree of the polynomial is odd and the leading coefficient is positive, the end behavior of the function is that the left end of the graph goes down and the right end goes up.

E. This statement is incorrect. As mentioned in D, the left end of the graph goes down and the right end goes up.

F. This statement is incorrect. The function is not a reflection of the parent function. It is a vertical stretch and a translation to the right.