Question

Which statement correctly describes the end behavior of y = -3x5 + 5x2 +2x + 1

A)
The graph rises to the left and falls to the right.


B)
The graph falls to the left and rises to the right.


C)
The graph rises to the left and rises to the right.


D)
The graph falls to the left and falls to the right.

Answer 1

For this we can observe term -3x^5 because it is x to power of 5 and for bit larger values of x in positive direction and x in negative direction it is dominant that other terms.

if x decreases because power 5 is odd, x^5 will be negative and when multiplied by -3 it will be positive so it will rise to the left steaper and steaper.

if x increases, x^5 increases quickly and when multiplied by -3 will be negative. which means that it falls to the right.

Answer is A)