Odd and Even Functions
Rucete Mathematics In a Nutshell
Even Functions
F(-x) = F(x)
The function remains unchanged when reflecting on the y-axis.
Odd functions
F(-x) = -F(x)
The function remains unchanged when 180° is rotated about the origin.
Neither odd and even function
Example
Even function
f(x) = x^2
f(-x) = (-x)^2 = (-x)(-x) = x^2
f(-x) = f(x)
Odd function
f(x) = x^3
f(-x) = (-x)^3 = (-x)(-x)(-x) = -x*3
f(-x) = -f(x)