Need help with some signals/systems [easy]

[cpatel23]

Hello.

Here is the question:
Are the following functions
a. linear or non linear
b. with memory or memoryless
c. causal or non causal
d. time invariant or time variant
e. stable or unstable

1. y(z) = x(z) + e^z
I know that this function is memoryless, causal, and unstable (infinite in range due to exponential).
I am not sure about linearity or time variance

2. ∑¹_i=-1x(z-i)
I know that this function has memory, causal, linear, stable (finite in range).
I don't know how to find if time variant or time invariant.

I would appreciate the help. My answers may be wrong as well.
Thanks :)

 

[cpscdave]

To test if a function is time invariant you need to check that
if x(t) = y(t)
then
x(t+k) = y(t+k)

so for question 2 expand the sumation and try the test :)