Which functions shows the function \( f(x)=3^{x} \) being translated 5 units down? \( f(x)=3^{x}+5 \) \( f(x)=3^{x}-5 \) \( f(x)=3^{x+5} \) \( f(x)=3^{x-5} \)

To translate the function \( f(x) = 3^x \) down by 5 units, you simply subtract 5 from the entire function. Therefore, the correct representation of the translation would be \( f(x) = 3^x - 5 \). This effectively lowers all output values of the function by 5. Understanding translations like this is important when visualizing functions. It not only helps you grasp how the graph shifts but also enhances your ability to manipulate and predict function behaviors in more complex scenarios! So, next time you’re working with functions, remember that adding or subtracting values shifts the graph up or down, while adding or subtracting inside the function affects the left or right movement!