Answer
(a) see graph,
(b) even,
(c) maximum $x=0, f(0)=1$, minimum $x=\pm2.54, f(\pm2.54)=-0.11$
Work Step by Step
(a) The graph of the function is shown in the figure.
(b) Based on the graph, it can be seen that this function is even, which can also be proved as follows
$f(-x)=\frac{cos(-x)}{1+(-x)^2}=\frac{cos(x)}{1+x^2}=f(x)$
(c) Based on the graph, it can be found that that maximum of the function is when $x=0, f(0)=1$,
and the minimum is when $x=\pm2.54, f(\pm2.54)=-0.11$ as shown in the figure.
