Question

What is the transformations needed to obtain `y = 17(sqrt(0.3x+3))` from the graph of `sqrt(x)`?

Answer 1

Vertical Stretch: 17
Horizontal Compression: .3
Horizontal Shift: -10

Explanation:

Using transformations of square root functions, we can see:

vertical shift = `sqrt(x) +k`,
horizontal shift = `sqrt(x-h)`,
vertical stretch/compression = `asqrt(x)`, and
horizontal stretch/compression = `sqrt(bx)`.

The formula `17sqrt(0.3x+3)` has a vertical stretch of 17 and a horizontal compression of 0.3. There is also no k, so the graph isn't shifted vertically.

To find the horizontal shift, however, we must divide `x-h` by 0.3 because we need 1x to find the right shift: `0.3x+3 = 0.3(x+10)`, so the horizontal shift is -10.