Question

The shape of f(x)=#sqrt(x) is moved 3 units upward and reflected in the y- axis. How I Do Solve this Problem?

Answer 1

Transformed `f(x) = -(sqrtx+3)`

Explanation:

First consider the "parent" graph `f(x)=sqrtx` shifted 3 unit positive ("up") on the `y-`axis. This will be the function `f(x)+3` so the first transformation `f_1(x) = sqrtx+3` and is shown in the graph below.

graph{sqrtx+3 [-20.27, 20.27, -10.13, 10.14]}

To reflect this function in the `y-`axis we simply replace it by its negative. So `f_2(x) = -f_1(x) = -(sqrtx+3)` shown in the graph below.

graph{-(sqrtx+3) [-20.27, 20.27, -10.13, 10.14]}

Hence, our transformed `f(x) = -(sqrtx+3)`