What is the initial value of the function represented by this table? x.    y  0.   51.   92. 130   34    5

Rearrange your table so that the smallest x comes first (goes on the first line) and the largest last (goes on the last line).  Identify the smallest x-value.  Here it seems as tho that value is 0.  The "initial value" of the function is the y-value corresponding to that "initial value."

In your table, '0' shows up twice as the x-value.  Thus, there is more than one y-value associated with the x-value '0.'  If that's the case, we must conclude that this table does not represent a function.