Answer
(a)
Odd Powers: Symmetric about the origin
Even Powers: Symmetric about the $y$-axis
(b) Please see below.
Work Step by Step
(a)
Looking at the graphs, we can find that the graphs of the odd power functions (red graphs) are symmetric about the origin while the graphs of the even power functions (blue graphs) are symmetric about the $y$-axis.
(b) By part (a) we can expect that the graph of the function $y=x^7$ (red graph) is symmetric about the origin and the graph of the function $y=x^8$ (blue graph) is symmetric about the $y$-axis.
