Fill in the blank.

Question

A function f is  when there exists a positive real number c such that f(t + c) = f(t) for all t in the domain of f.

Answer 1

first impression is that f(t) is a constant function, like f(t)=10

thinking more though and looking at William W. diagram,

it comes to mind that f(t) could be a periodic function.

say f(t)=sin(t) and c=2π and let domain be all real numbers

then f(t+c)=f(t)

Answer 2

To help, I drew a little sketch:

For any value of "t", we see that the function value of f(t + c) is always the same as f(t). And if you pick a different value for "t" and a different "c", the function value is still the same. So, basically, whatever "t" you pick the function value will not change for a larger "t".

Does that help?