Question

Find the function that is finally graphed after the following transformations are applied to the graph of y = √x in the order listed.(1) Shift down 7 units(2) Reflect about the x-axis(3) Reflect about the y-axis

Answer 1

Given the function:

`y=\sqrt[]{x}`

we will find the function that results from the following transformations:

(1) Shift down 7 units

so, the result will be:

`y=\sqrt[]{x}-7`

(2) Reflect on the x-axis

so, the rule of reflection will be: (x,y) →(x, -y)

so, the function will be:

`y=-\sqrt[]{x}+7`

(3) Reflect on the y-axis

so, the rule of reflection will be: (x,y) →(-x, y)

So, the function will be:

`y=-\sqrt[]{-x}+7`