The parent function \( f(x)=3^{x} \) has been shifted to the left 2 units, reflected vertically over the \( x \)-axis and shifted up 5 units. What equation models the transformed graph? \( f(x)=3^{x-2}-5 \) \( f(x)=-3^{x+2}-5 \) \( f(x)=-3^{x-2}+5 \) \( f(x)=-3^{x+2}+5 \)

To model the transformed graph of the parent function \( f(x) = 3^x \), we follow a series of transformations. Shifting the function left by 2 units involves changing \( x \) to \( x + 2 \). Reflecting it vertically over the \( x \)-axis changes the sign of the function, leading to a multiplication by -1. Finally, shifting up by 5 units adds 5 to the function. So the correct transformation steps yield the equation \( f(x) = -3^{x+2} + 5 \). In essence, this transformation journey is like taking a roller coaster ride! You start at point zero (the original function), zip left a bit (shift), take a thrilling flip (reflection), and then soar high in the sky (shift up) for a breathtaking view! Always remember to watch for those signs—it’s a wild ride!