How do you describe the end behavior for #f(x)=-x^5+4x^3-2x-2#?
1 Answer
Left side up, right side down
Explanation:
There are two steps to describing the end behavior of a polynomial:
- Determine the behavior of the right (
#+x# "side") of the graph - Determine the behavior of the left (
#-x# "side") of the graph
Right Side Behavior
Determining the right side behavior of the graph involves looking at the leading coefficient, or the coefficient of the highest power of
If the leading coefficient is negative, then the right edge of the graph points downward toward the negative
For this problem, we say the right edge is pointing downward.
Left Side Behavior
Determining the left side behavior of the graph involves looking at the highest power of
For this problem, the highest exponent is 5 (from
Check with the graph
You can verify with the graph:
graph{-x^5+4x^3-2x-2 [-3.24, 3.23, -7.12, 7.12]}