Final answer:
The polynomial's degree is 7, it is not in standard form, and we cannot determine similarity to f(x) = -x without more context. Additionally, we cannot assert that the elevator only goes up without coming back down, as polynomials can have complex end behaviors.
Step-by-step explanation:
The student's question pertains to the characteristics of a polynomial function that represents the height of an elevator over time. By examining the given polynomial 6x5 + 18x7 + 11, we can address the true statements about the function.
- A) The degree of the polynomial is indeed 7, since the highest power of the variable x is 7 in the term 18x7.
- B) The polynomial is not in standard form because the terms are not ordered from highest to lowest degree. The standard form should be 18x7 + 6x5 + 11.
- C) Without a clear definition of 'similar,' we cannot conclusively say whether the start and end of the trip are similar to f(x) = -x.
- D) Because polynomials describe smooth, continuous functions, and because the leading term of a polynomial determines its end behavior, we can say that, without knowing specific constraints on the variable x (time), the elevator modeled by this polynomial could go up and come back down as x increases, contrary to the assertion that it only goes up.