Graph the function.
Use the graph of $f(x)=4^{x}$ to obtain the graph of $g(x)=4^{x-3}-2$.
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Step 1 ：Start with the graph of the function \(f(x)=4^{x}\), which is an exponential function with a base of 4. It passes through the point (0,1) and increases as x increases.

Step 2 ：To obtain the graph of \(g(x)=4^{x-3}-2\), apply two transformations to the graph of \(f(x)=4^{x}\).

Step 3 ：The first transformation is a horizontal shift to the right by 3 units, represented by the \(x-3\) in the exponent. This moves every point on the graph of \(f(x)=4^{x}\) 3 units to the right to obtain the graph of \(4^{x-3}\).

Step 4 ：The second transformation is a vertical shift down by 2 units, represented by the \(-2\) outside the exponent. This moves every point on the graph of \(4^{x-3}\) 2 units down to obtain the graph of \(g(x)=4^{x-3}-2\).

Step 5 ：Therefore, the point (0,1) on the graph of \(f(x)=4^{x}\) is moved to the point (3,-1) on the graph of \(g(x)=4^{x-3}-2\).

Step 6 ：The shape of the graph does not change. It still increases as x increases, but it now passes through the point (3,-1) instead of the point (0,1).

Step 7 ：\(\boxed{\text{Therefore, the graph of } g(x)=4^{x-3}-2 \text{ is the graph of } f(x)=4^{x} \text{ shifted 3 units to the right and 2 units down.}}\)