Which of the following polynomials could have the same end behavior as f(x)=ax^6+bx^5+c?

Question

There may be more than one correct answer. Select all correct answers.

a. nx^5+bx^4+c

b. kx+b

c. dx^4−bx^3−cx^2+dx+e

d. −jx^8+bx^7+cx^4

e. −mx^2

can someone help me with this it is confusing and there is more than one answer so yea i need help

Answer 1

all polynomials of even degree either
go up on both ends
or do down on both ends,
depending on the sign of a.

Odd-degree polynomials go up on one end, and down on the other.

So, since f(x) is of degree 6 (even), any even-degree polynomial whose leading coefficient is the same sign as a will behave like f(x) at the ends.

So, C,D,E are possibilities. If all constants a,b,c,... are positive, then only C will do.