8. Write the equation described by the following transformations:
Parent Function : $f(x)=4^{x}$
Shifted left 5 units and up 3 units
Vertical Compression by $\frac{1}{2}$

Step 1 ：The parent function is \(f(x)=4^{x}\).

Step 2 ：The function is shifted left 5 units, which can be represented by replacing \(x\) with \((x+5)\) in the parent function.

Step 3 ：The function is shifted up 3 units, which can be represented by adding 3 to the parent function.

Step 4 ：The function is vertically compressed by \(\frac{1}{2}\), which can be represented by multiplying the parent function by \(\frac{1}{2}\).

Step 5 ：Applying these transformations to the parent function gives the transformed function as \(g(x)=\frac{1}{2}f(x+5)+3\).

Step 6 ：Substituting the parent function into the transformed function gives \(g(x)=\frac{1}{2}*4^{x+5} + 3\).

Step 7 ：\(\boxed{g(x)=\frac{1}{2}*4^{x+5} + 3}\) is the equation described by the transformations.