Describe the end behavior of the function - Explain and Show Work

Question

f(x)=x^5 - 3x^3 + 3x + 2

Answer 1

In any polynomial function:

The leading term, X⁵ in this polynomial, will always dominate

what happens to the curve when X approaches infinity and

when X approaches negative infinity

 

as  X approaches positive infinity:  X⁵ will go to positive infinity;

therefor the curve goes up to positive infinity

 

as X approaches negative infinity:  X⁵ will go to negative infinity;

therefor the curve goes down to negative infinity

 

 

Answer 2

This is a positive odd polynomial function.

 

Increases in the interval (-∞, least x-intercept)

Increases in the interval (highest x-intercept, ∞)

 

You can graph this on your calculator to verify.  The same can be done for the other problem you posted.