I've never encountered a function definition like this before and am wondering how you would go from this definition to finding out what features it has (y-intercept, even/oddness, min/max value, periodicity).
Definition for $f$
If the remainder of $x$ divided by 3 is 0, then $f(x)=11$.
If the remainder of $x$ divided by 3 is 1, then $f(x)=−7$.
If the remainder of $x$ divided by 3 is 2, then $f(x)=2$.
Assuming that function is defined over set of Natural number N (as otherwise definition doesn't make much sense). You can look at its various properties viz. maxima is 11 (occurs at x : x=0(mod3)), and minima is -7 (occurs at x:x=1(mod 3)). You can check that function is neither even nor odd look at f(5) and f(-5). function is periodic with period 3 (verify !). and by y-intercept if you mean f(0) then you can see y-intercept=f(0)=11.
