Algebra/Chapter 11/Extrema and Continuity

An even function is defined as a function ${\displaystyle f}$ such that ${\displaystyle f(-x)=f(x)}$.
Geometrically an even function can be defined as a function that exhibits a mirror image symmetry across the y-axis (the vertical line that passes through the origin).

An example of an even function is ${\displaystyle h(x)=x^{2}}$ because ${\displaystyle f(5)=25=f(-5)}$ and because ${\displaystyle f(x)=x^{2}=f(-x)}$ for all real numbers x.

An odd function is defined as a function ${\displaystyle f}$ such that ${\displaystyle f(-x)=-f(x)}$.
Geometrically an odd function can be defined as a function that exhibits a 180 degree rotational symmetry about the origin.

An example of an odd function is ${\displaystyle f(x)=x^{3}}$ because for all real numbers x, ${\displaystyle f(x)=x^{3}=-((-x)^{3})=-f(-x)}$ for example ${\displaystyle f(2)=2^{3}=8=-((-2)^{3})=-(-8)=-((-2)^{3})=-f(-2)}$