Describe the transformation of the square root function.

Question

Describe the transformations of the following square root function.  y=2√x-3 +4

Answer 1

Hi Luisa!

The standard form of the square root function is:

y= a√b(x-h) + k

a is the vertical stretch/compression factor

1/b is the horizontal stretch if 0< b < 1 /shrink if b>1 factor

-h means right h units

+h left h units

+ k up k units

-k down k units

Your function y=2√x-3 +4 tells three things.

a= 2 since a > 1 then it’s a vertical stretch factor of 2

1/b = 1 so no horizontal stretch or compression

-3 means it’s being shifted 3 units right

+ 4 means it’s being shifted up 4 units

So the transformations are: vertically stretched by a factor of 2, right 3 up 4.

I hope this helps. Have a great day!

Mrs. S

Answer 2

If the original function was y = 2√x, then function y = 2√x-3 + 4 will be positioned in relation to the original function as following:

1. shifted 3 units to right along the axis "x"
2. shifted 4 units up along the axis "y"