Is this input function time varying?
Signals are (almost) always time variant. Otherwise they would be very boring :-). I believe your question is about whether "systems" are time invariant or not. A system basically is a "prescription" of how to create an output signal from an input signal. The equation you show is a system equation of how to create output y[n] from input x[n].

The idea of time invariance is the following: The behavior of the system doesn't depend on absolute time, i.e. the relationship between input and output is the same, regardless of whether it's Tuesday or Friday. You can find a more mathematical description here http://en.wikipedia.org/wiki/Time-invariant_system 

The easiest invariance test is the following:


pick any input signal, typically $\delta [n]$ will do fine.
Calculate the output $y{_{0}}[n]$ for that intput
now delay the input signal by some amount. 
Calculate the output $y{_{1}}[n]$ for the delayed input
If $y{_{1}}[n]$ is NOT simply a delayed version of  $y{_{0}}[n]$ then the system time variant


Another (equivalent) test is the following


For time invariant system, the system equations only dependency on time must be as linear index into the input signal


Either one will work.