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