A reflection over the y-axis
An horizontal translation of 5 units to the right
A vertical stretch of 2
A vertical translation of 3 units up
Explanation:
[tex]\begin{gathered} \text{Parent function: }\sqrt[]{x} \\ A\text{ reflection over the y ax is: (x, y) }\rightarrow\text{ (-x, y)} \\ A\text{ reflection over the y ax is = }\sqrt[]{-x} \end{gathered}[/tex][tex]\begin{gathered} An\text{ }horizontal\text{ translation of 5 units to the right: } \\ y\text{ = f(x) - d, where d = 5} \\ \text{ }A\text{ translation of 5 units to the right = }\sqrt[]{-x-5} \end{gathered}[/tex][tex]\begin{gathered} \text{Vertical stretch of 2: enlargement by a scale factor of 2} \\ \text{Vertical stretch of 2 = }2\times\text{ }\sqrt[]{-x-5} \\ \text{Vertical stretch of 2 = }2\text{ }\sqrt[]{-x-5} \end{gathered}[/tex][tex]\begin{gathered} \text{Vertical }Translation\text{ of 3 units up: } \\ y\text{ = f(x) + 3} \\ Translation\text{ of 3 units up = }2\text{ }\sqrt[]{-x-5}\text{ + 3} \end{gathered}[/tex]
Transformations on the parent function:
A reflection over the y-axis
An horizontal translation of 5 units to the right
A vertical stretch of 2
A vertical translation of 3 units up
