Question

find the function that is finally graphed after given the following transformations is applied to the graph of y = √ x in the order stated.

(1) Shift up 2 units
(2) Reflect about the x-axis
(3) Reflect about the y-axis

Answer 1

Step 1:

The function is .

(1)

Shifts upward units :

To obtain the graph of , shift the graph of a distance units upward.

Add units to the function , thus .      

Step 2 :

(2)

Reflects about the - axis :

reflects about the - axis.

Multiply with , thus .

Step 3 :

(3)

Reflects about - axis :

reflects about the  - axis.

Substitute  in , thus .

Solution :

The function is .