Chapter 4.6, Problem 80E

Investigation Consider the function

$f(x)=\frac{2x^n}{x^4+1}$

for nonnegative integer values of n.

(a) Discuss the relationship between the value of n and the symmetry of the graph.

(b) For which values of n will the x-axis be the horizontal asymptote?

(c) For which value of n will $y=2$ be the horizontal asymptote?

(d) What is the asymptote of the graph when $y=2$

(e) Use a graphing utility to graph f for the indicated values of n in the table. Use the graph to determine the number of extrema M and the number of inflection points N of the graph.

n	0	1	2	3	4	5
M
N