Question

Rewrite y =V9x +45+ 2 to make it easy to graph using a translation. Describe the graph.Rewritten, y = 3 VX+5+ 2. It is the graph of y = 3 VX translated 5 units left and 2 units up.Rewritten, y = VX+5+ 2. It is the graph of y = V translated 5 units right and 2 units up.Rewritten, y == VX-5+ 2. It is the graph of y = Vx translated 5 units left and 2 units up.>Rewritten, y = 3 VX+5+ 2. It is the graph of y = 3 V translated 5 units right and 2 units up.

Answer 1

`It\text{ is the graph of y = 3}\sqrt[]{x},\text{ 5 units to the left }and\text{ 2 units up (option A)}`

`\begin{gathered} y\text{ = }\sqrt[]{9x\text{ + 45}}\text{ + 2} \\ y\text{ = }\sqrt[]{9(x\text{ + 5)}}\text{ + 2} \\ y\text{ = 3}\sqrt[]{x+5}\text{ + 2} \end{gathered}`
`\begin{gathered} \text{for }y\text{ = f(x)} \\ y\text{ = f(x - k) , translation to the right} \\ y\text{ = f(x + k), translation to the left} \\ y\text{ = f(x) + d, translation up} \\ y\text{ = f(x) - d, translation down} \end{gathered}`
`\begin{gathered} y\text{ = }3\sqrt[]{\text{x + 5}},\text{ tranlsation }to\text{ the left} \\ y\text{ = }3\sqrt[]{\text{x + 5}}\text{ + 2 , 2 is translation up} \\ \text{Hence, }y\text{ = }3\sqrt[]{\text{x + 5}}\text{ + 2 } \\ It\text{ is the graph of y = 3}\sqrt[]{x},\text{ 5 units to the left }and\text{ 2 units up (option A)} \end{gathered}`