Final answer:
The function that represents the function f(x) = 3^x translated 5 units to the left is f(x) = 3^(x+5). This is achieved by substituting x with x + 5 in the original function, without altering the shape of the graph.
Step-by-step explanation:
The question is asking which function represents the function f(x) = 3^x being translated 5 units to the left on the x-axis. To translate a function to the left by 5 units, we substitute x with x + 5. The correct function that shows this translation is f(x) = 3^(x+5).
To check that this is a translation and not a stretch, compression, or reflection, it is important to note that the base of the exponent remains unchanged and we are only adding 5 to the variable x. Therefore, the transformation does not affect the shape of the graph in any way other than shifting it horizontally.