Analyze the graphs \( g(x)=-4 \sqrt{x+1}+3.5 \) and \( h(x)=-4 \sqrt{x+1}-4.5 \). Which option correctly describes the transformation to take \( g(x) \) to \( h(x) \) ? (1 point) vertical translation right 8 units vertical translation down 8 units vertical translation up 8 units vertical translation down 7 units

To transform \( g(x) \) into \( h(x) \), we notice that \( g(x) \) is shifted downwards. Specifically, \( h(x) \) is derived by subtracting \( 8 \) from \( g(x) \)'s maximum point, so the correct transformation is a vertical translation down 8 units. This transformation can be visualized by considering the initial position of the graph of \( g(x) \) at \( y = 3.5 \) and moving it directly downward to land at \( y = -4.5 \). Stretching the concept of a graph, it’s like taking a lovely balloon bouquet you just lifted to a nice height and letting it float slowly down to a cozy, lower level! 🎈