Question

The equation of the image is .
y=-2 (square root 3x -12) -5
What is the base (original) function?

Describe the series of transformations.

Write the image in the function notation, y = af[k(x - p)] + q.

Answer 1

I assume that the base function is the parent function. This is y = f(x) = sqrt(x). I'll revise the equation slightly:

\[y=-2\sqrt{3x-12}-5=-2\sqrt{3(x-4)}-5\]

The image in function notation is:
\[y=-2f(3(x-4))-5\]

The transformations undergone here include a vertical stretch by a factor of 2. Also, the image flips reflects over the x-axis (turns upside down). The horizontal stretch is 1/3 (since this "stretch" is less than 1, the image is actually compressed). The image is shifted to the right 4 places and down 5 places.