Q:

How do I generate a table of data points from a function and add random noise?

I am trying to generate a table of data for the function: 
f(x) := (Sin[2 Pi t]) (1 + (1/5) Sin[6 Pi t] + (1/10) Sin[8 Pi t])
Table[Plot[f[t], {t, -5, 5}, ImageSize -> {150, 150}], {t, -5, 5}] 

I believe I plotted it correctly by using this syntax tp define the function and
make the plot, but I am not sure if I am doing this correctly. 
Also, I want to add random noise,but I do not know how.

A:

This post is a partial answer, directed at your question about your syntax, which is incorrect as posted.
In Mathematica, a function function of one variable t is defined with the syntax f[t_] := ..., not f(t) = .... Note the square brackets [ ] and the underscore _ after the the t which identifies t as a variable.
Further, I don't understand why you introduced Table when making your plot. Do you really want 11 copies of the plot? Because that's what your Table expression will deliver.
Here is the correct syntax for what I think you really want:
f[t_] := (Sin[2 Pi t]) (1 + (1/5) Sin[6 Pi t] + (1/10) Sin[8 Pi t])

Plot[f[t], {t, -5, 5}, ImageSize -> {150, 150}]

which will produce the Output

The part of your question concerning randomizing your data has been answered before in this question.

