Question

even functions
a function is even when
★ it has symmetry with respect to the
across the
★ =f(x) for all values of x (when you plug in
which you began.
★ examples of even functions

note: functions with even exponents (powers) may or may not be even functions. just because a function has an even power, does not mean it is an even function.

odd functions
a function is odd when
★ it has point symmetry about the origin (the graph stays the same after a
★ = -f(x) for all values of x (when you plug in
with which you began.
★ examples of odd functions

note: functions with odd exponents (powers) may or may not be odd functions. just because a function has an odd power, does not mean it is an odd function.

Explanation:

For even - functions: A function is even when it has symmetry with respect to the y - axis (the graph does not change when reflected across the y - axis), $f(-x)=f(x)$ for all values of $x$ (when you plug in $-x$, you get back the same function with which you began).
For odd - functions: A function is odd when it has point symmetry about the origin (the graph stays the same after a 180 - degree rotation about the origin), $f(-x)=-f(x)$ for all values of $x$ (when you plug in $-x$, you get back the negation of the function with which you began).

Answer:

Even functions:

• Symmetry: y - axis
• Equation: $f(-x)=f(x)$
• Input value: $-x$

Odd functions:

• Symmetry: origin
• Equation: $f(-x)=-f(x)$
• Input value: $-x$