Question

Using the parent function g(x)=x√, write the equation for a graph that has been moved 5 units left, is three times as tall, and has been reflected over the x-axis. Be sure to also explain your response in words.

Answer 1

The given parent function is,

`g(x)=\sqrt[]{x}`

The transformation of the above g(x) is,

`g^(\prime)(x)=-a\sqrt[]{x+h}\text{ }`

Here, the parent function g(x) is shifted h units to the left .

If a is greater than 1, then g(x) is streched vertically by a units.

Since the function is multiplied by -1 , g(x) is reflected across the x axis.

To shift the graph of g(x) 5 units left, 3 times as tall and reflect across the x axis,

we take k=5, a=3 and put it in g'(x).

`g^(\prime)(x)=-3\sqrt[]{x+5}`

So, the equation of a graph that has been shifted, 5 units left, is 3 times as tall and reflected across the x axis is,

`g^(\prime)(x)=-3\sqrt[]{x+5}`