(1) Describe the transformations that occurred from the parent function, \( y=\sqrt{x} \). Then determine the new domain and range. \( \begin{array}{ll}\text { a) } y=\sqrt{x+5} & \text { b) } y=-\sqrt{x-3}\end{array} \)

For \( y = \sqrt{x+5} \), the transformation involves a horizontal shift to the left by 5 units. This means that instead of starting from \( x=0 \) (the original domain), the new domain becomes \( x \geq -5 \). The range remains unchanged as \( y \geq 0 \). For \( y = -\sqrt{x-3} \), the transformation includes a horizontal shift to the right by 3 units and a vertical reflection over the x-axis. The new domain is \( x \geq 3 \), and the range flips to \( y \leq 0 \), indicating that the function only takes negative values.