Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is (a) even and (b) odd.?

(4,9)

For odd function:
 f(x) = - f(-x). 

For function is even,
 f(x) = f(-x). 

using the above laws 
for odd function:
 f(4) = 9 = - f(-4)
f(-4) = -9
so the second  point is (-4,-9) 

for even function: f(4) = 9 = f(-4)
 so the second point is (-4,9)

Your answer is 57 ok