The parent function is 2^x.
Simplify the transfered function to obtain it as parent function.
[tex]\begin{gathered} 2^{x-2}-6=2^x\cdot2^{-2}-6 \\ =\frac{2^x}{4}-6 \end{gathered}[/tex]
On comparison transfered function with parent function, it can be observed that for same value of x, the value of y from transfered first decreases by the factor of 4 and 6 is subtracted from the resultant value.
After ploting the graph same thing can be observed at particular value x. The value of y coordinate in transfered function is one fourth of y from parent function with 6 unit shifted downward.
