pescribe the transformations of each function: 9. \( y=4 \sqrt{x+2}-3 \)

The function \( y=4 \sqrt{x+2}-3 \) involves a series of transformations starting with the basic square root function \( y=\sqrt{x} \). First, we shift the graph 2 units to the left due to the \( +2 \) inside the square root. Then, the coefficient \( 4 \) outside stretches the graph vertically, making it grow faster. Lastly, the \( -3 \) translates the entire graph down by 3 units, giving it a new position on the y-axis. To visualize these changes, imagine the square root function starting at the origin. After shifting it left, it starts at the point (-2,0), then stretches up four times faster (think of taller hills!). Lastly, with the downward shift, the peak drops down to the point (-2,-3). So, you get a whole new landscape of the square root function!