Is this input function time varying?

1. How do you determine if a system is time varying?
2. How do you know if a signal is time-invariant?
3. Which one is a time varying response?

How do you determine if a system is time varying?

A system is said to be time invariant if the response of the system to an input is not a function of time. On the other hand a system is time variant if the response to an input alters with time i.e. the system has varying response to the same input at different instants of time.

How do you know if a signal is time-invariant?

A system is time-invariant if its output signal does not depend on the absolute time. In other words, if for some input signal x(t) the output signal is y1(t)=Trx(t), then a time-shift of the input signal creates a time-shift on the output signal, i.e. y2(t)=Trx(t−t0)=y1(t−t0).

Which one is a time varying response?

A time-variant system is a system whose output response depends on moment of observation as well as moment of input signal application. In other words, a time delay or time advance of input not only shifts the output signal in time but also changes other parameters and behavior.