Use transformations to graph the function. Determine the domain, range, horizontal asymptote, and $y$ intercept of the function.
\[
f(x)=3^{x-3}
\]

Use the graphing tool to graph the function
(For any answer boxes shown with the grapher, type an exact answer)

Step 1 ：The function is an exponential function with base 3. The graph of the function \(f(x) = 3^x\) is transformed by shifting 3 units to the right to get the graph of the function \(f(x) = 3^{x-3}\).

Step 2 ：The domain of the function is all real numbers because we can substitute any real number for \(x\) in the function.

Step 3 ：The range of the function is all positive real numbers because the base of the exponential function is greater than 1.

Step 4 ：The horizontal asymptote of the function is \(y = 0\) because as \(x\) approaches negative infinity, \(f(x)\) approaches 0.

Step 5 ：The \(y\) intercept of the function is the value of the function at \(x = 0\). We can find this by substituting \(x = 0\) into the function.

Step 6 ：Let's calculate the \(y\) intercept. \(f = 3^{(x - 3)}\) where \(x = 0\). So, \(f = 3^{(0 - 3)} = 3^{-3} = \frac{1}{27}\).

Step 7 ：Final Answer: The domain of the function is all real numbers. The range of the function is all positive real numbers. The horizontal asymptote of the function is \(y = 0\). The \(y\) intercept of the function is \(\boxed{\frac{1}{27}}\).