how can we show an antiperiodic function?

Question

How can we graphically show an anti-periodic function? I can't imagine. Maybe I have got no imagination...!! for example we can show the sin and cos or other periodic functions on the graphs. is it the possible for an anti-periodic one?

Answer 1

$f(x+p)=-f(x)$ then its anti-periodic

(to see intuitively graphically its like an odd function which is also periodic )

all anti-periodic functions with period $p$ are periodic with period $2p$

not all periodic functions have corresponding anti-periodic function

but all anti-periodic functions are periodic

it is enough to show that your function is periodic and odd with when shifted by half of the period.

example http://www.wolframalpha.com/input/?i=sin%28x%2Bpi%29

$sinx$ is periodic with $2\pi$ period so you check if $sin(x+\pi)=-sinx$ if it is then its anti-periodic with period $\pi$