Determine the end behavior of the following polynomial functions.

Question

a) P(x) = 4x⁵− 3x⁴ + 9x² + 10
b) Q(x) = −3x⁶+ 80
c) Z(x) = 9x³+ 6x² − 5x + 8

Answer 1

a)

 

The leading term is positive and has an odd exponent.  Therefore, the curve decreases as x approaches negative infinity and increases infinitely as x approaches positive infinity.

 

 

b)

 

Leading term is negative with even exponent.  The curve decreases as x approaches both negative infinity and positive infinity.

 

 

Try part c on your own.  If you look at the graph references in your textbook, you will be able to get the answer.