Which set of steps will translate \( f(x)=6^{x} \) to \( g(x)=6^{x-5}-7 \) ? Shift \( f(x)=6^{x} \) five units to the left and seven units up. Shift \( f(x)=6^{x} \) five units to the right and seven units down. Shift \( f(x)=6^{x} \) seven units to the right and five units up. Shift \( f(x)=6^{x} \) seven units to the left and five units down.

To translate the function \( f(x) = 6^{x} \) to \( g(x) = 6^{x - 5} - 7 \), you start by shifting it horizontally and then vertically. First, the expression \( x - 5 \) indicates a shift to the right by 5 units (this is because subtracting a number in the function argument moves the graph to the right). Next, the "-7" outside the function represents a downward shift of 7 units. So the correct answer involves a shift to the right and down. Lastly, did you know that exponential functions are used in various fields, from finance for calculating compound interest to biology for modeling population growth? They really do pop up everywhere! Understanding how to shift these functions allows you to manipulate data and find applications in real-life situations. Whether you’re plotting a graph for a science project or analyzing trends in stock rates, knowing your transformations makes all the difference!