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 up 4 units (2) Reflect about the x-axis (3) Reflect about the y-axis y=0

Answer 1

Solution;

The function is

y =

a) shift up 4 unit then the function is

$y= \sqrt{x}+4$

b) Reflect about x_axis that means vertical reflect

So after reflect the function is

$y= -(\sqrt{x}+4)$

C) reflect about y_axis that means horizontal reflect

And after reflect the function is

$y= -(\sqrt{-x}+4)$

The answer is

$y= -(\sqrt{-x}+4)$