Question

Find an equation for the graphed function below by using transformations of the grade h of a toolkit function.

Answer 1

$y^{}=\sqrt[]{x-1}\text{ +2}$

Explanation

Step 1

the original function is

$y=\sqrt[\square]{x}$

we can see that the original function was shifted

a) one unit to the rigth

b) 2 units up

so

Step 2

A) shifted one unit to the right:

To shift, move, or translate horizontally, replace y = f(x) with y = f(x + c) (left by c) or y = f(x - c) (right by c).so

C=1, to the rigth, so f(x-1)

replace

$\begin{gathered} y=\sqrt[]{x} \\ y^{\prime}=\sqrt[]{x-1} \end{gathered}$

Step 3

B)now, shifted 2 units up.

To move a function up, you add outside the function: f (x) + b is f (x) moved up b units. Moving the function down works the same way; f (x) – b is f (x) moved down b units.

hence,

$\begin{gathered} y^{\prime}=\sqrt[]{x-1} \\ b=2,so \\ y^{\prime}^{\prime}=\sqrt[]{x-1}\text{ +2} \end{gathered}$

therefore, the answer is

$y^{}=\sqrt[]{x-1}\text{ +2}$

I hope this helps you