(1.4) Transforming Parent Functions
1. Identify the parent function and the transformations in each of the following (in the correct order):
(a) ${ }^{f} y=-\frac{2}{x+3}+4$
(b) $y=-(2)^{2 x+2}+3$
(c) $y=5-2|3 x+6|$
(d) $y=7+3 \sqrt{\frac{1}{2} x-1}$

Step 1 ：The parent function for (a) is \(y=\frac{1}{x}\). The transformations are reflection in the x-axis, vertical stretch by a factor of 2, horizontal shift 3 units to the left, and vertical shift 4 units up.

Step 2 ：The parent function for (b) is \(y=2^x\). The transformations are reflection in the x-axis, horizontal compression by a factor of 2, horizontal shift 1 unit to the left, and vertical shift 3 units up.

Step 3 ：The parent function for (c) is \(y=|x|\). The transformations are vertical stretch by a factor of 2, horizontal compression by a factor of 3, horizontal shift 2 units to the left, and vertical shift 5 units up.

Step 4 ：The parent function for (d) is \(y=\sqrt{x}\). The transformations are vertical stretch by a factor of 3, horizontal stretch by a factor of 2, horizontal shift 1 unit to the right, and vertical shift 7 units up.

Step 5 ：\(\boxed{\text{Final Answer:}}\)

Step 6 ：For (a), the parent function is \(y=\frac{1}{x}\) and the transformations are reflection in the x-axis, vertical stretch by a factor of 2, horizontal shift 3 units to the left, and vertical shift 4 units up.

Step 7 ：For (b), the parent function is \(y=2^x\) and the transformations are reflection in the x-axis, horizontal compression by a factor of 2, horizontal shift 1 unit to the left, and vertical shift 3 units up.

Step 8 ：For (c), the parent function is \(y=|x|\) and the transformations are vertical stretch by a factor of 2, horizontal compression by a factor of 3, horizontal shift 2 units to the left, and vertical shift 5 units up.

Step 9 ：For (d), the parent function is \(y=\sqrt{x}\) and the transformations are vertical stretch by a factor of 3, horizontal stretch by a factor of 2, horizontal shift 1 unit to the right, and vertical shift 7 units up.