Question

Determine the end behavior of the polynomial function. f(x)=-3x^4-2x^3+2x^2+ 3x +5 a) falls to the left and rises to the right b) falls to the left and falls to the right c) rises to the left and rises to the right d) rises to the left and falls to the right e) none

Answer 1

Option b is correct

Explanation:

In order to check the end behavior of a polynomial function we just check the leading term and its coefficient and the procedure is as follows:

Here we can see that highest exponent of the polynomial function is 4

therefore degree of the polynomial is 4. and therefore
`-3x^4` is leading term.

because of even degree it will be same from both ends that is either both sides rises or both sides falls. Since number in the front of leading is negative therefore it falls at both ends. that is falls to the left and falls to the right.

therefore option b is correct.