Question

The graph of f(x)= x^2 is transformed by a vertical reflection, then a horizontal compression by a factor of 2, then a horizontal translation 3 units to the right, and finally a vertical translation of 5 units up.

-What is the equation of the transformed function?

-What is the domain and range of the transformed function?

Answer 1

If g(x) is the transformed function, then

`g(x) = - f\big( ~2 (x-3)~ \big) + 5`

or

`g(x) = - \big( ~2 (x-3)~ \big)^2 + 5`

The domain is still all real numbers, (-infty, infty).

The range is (-infty, 5], since it was reflected vertically and then translated up by 5 units.