a.
Given y = -|x - 2| + 3
parent function is y = | x|
The transformation goes thus
Horizontal shift to the right by 2 units
Reflection over the x-axis
Vertical shift upward by 3 units
b.
[tex]\begin{gathered} \text{ Given }f(x)=5(x+3)^2-12 \\ \text{parent function = f(x) = }x^2 \\ \text{ The transformation is } \\ \text{Horizontal shift to the left by 3 units } \\ \text{Vertical stretch by 5 units } \\ Vertical\text{ shift downward by 12 units} \end{gathered}[/tex]
c.
[tex]\begin{gathered} \text{ Given }g(x)=3-(x-1)^3 \\ \text{parent function is g(x) = x}^{3^{}^{}} \\ \text{ The transformation is } \\ \text{Horizontal shift to the right by 1 unit} \\ \text{ Horizontal reflection} \\ \text{ Vertical shift upward by 3 units} \end{gathered}[/tex]
