1. The problem asks us to find the equation of a function $g(x)$ that shifts the graph of $f(x) = 2^x$ right by 5 units and down by 3 units. 2. The general rule for shifting a function $f(x)$ is: - To shift right by $h$ units, replace $x$ with $x - h$. - To shift down by $k$ units, subtract $k$ from the function. 3. Applying these shifts to $f(x) = 2^x$: - Shift right 5 units: $f(x - 5) = 2^{x - 5}$ - Shift down 3 units: $g(x) = 2^{x - 5} - 3$ 4. Therefore, the equation of the shifted function is: $$g(x) = 2^{x - 5} - 3$$ This means the graph moves 5 units to the right and 3 units down compared to the original $f(x)$.