Can a function be both even and odd? use algebra to find the answer.

• if f(x) is an even number, then f(-x) = ? for all x.
• if f(x) is an odd number, then f(-x) = ? for all x.
• by the transitive property of equality, this means that f(x) = -f(x)
• combine like terms in the equation f(x) = -f(x)
= 0
divide both sides by 2.
f(x) =

• this function is both even and odd. in fact, it is the only function that is both even and odd. describe the function's graph, and state how it proves your conclusion.

fill in what the "? ? " are. you, much appreciated.