What effect does multiplying the function \( f(x) = 3^x \) by -1 have on its graph? Describe any transformations.

When you multiply the function \( f(x) = 3^x \) by -1, the graph undergoes a reflection across the x-axis. This means that instead of being above the x-axis (for all \( x \), as \( 3^x \) is always positive), the graph of \( -f(x) = -3^x \) will be below the x-axis for all values of \( x \). To illustrate this, while the original function approaches zero from above as \( x \) approaches negative infinity, the transformed function will approach zero from below, creating a symmetrical counterpart to the original graph. This simple change flips the positive peaks of the exponential into negative ones, making for a striking visual transformation!