How are even & odd functions alike? How different?

Answer 1

similarities
both are functions
both have the final answer of same magnitude

disimilarities
if f is an even function then f(-x) = f(x)
so if f is defined as f(x) = x^2 then
f(-3) = (-3)^2 = 9
also f(3) = 9

if g is an odd function then f(-x) = -f(x)
so if g is defined as g(x) = x^3
g(-2) = (-2)^3 = -8
but g(2) = 8

f(-3) = f(3)
g(-2) = -g(2)

Answer 2

An even function, like the cosine function, gets its name by the fact that its McLaurin expansion has only even powers of the variable. Equally odd functions, such as the sine function, only have odd powers in their McLaurin expansions. An even function has reflective symmetry about the y axis. An odd function has rotational symmetry about the origin.
How they are different is obvious. How are they alike? Well, I suppose the fact that both have some sort of symmetry and special expansions. More than that I don't know.

Answer 3

►Difference
even functions are symmetry with respect to y axis;
it means:
f(-x) = f(x)

Odd functions are symmetry with respect to origin;
it means:
f(-x) = -f(x)

►similarity:
+Both are functions
+ their domain should be completely symmetric;

it means that: for example
(-5 5] isnot a domain for even or odd functions
whereas:
(-5 5) or [-5 5] can be the domain for even or odd functions

+their derivatives give one another;
it means the derivative of an even function is Odd function & also
it means the derivative of an Odd function is even function

Answer 4

difference:
odd function line symetrical in the y-axis
even point symetrical in the origin.

alike ???