Question

Given g(x) = -3√−2x + 4 + 5, State the transformations on the parent function f(x) = x2 and write g(x) in function notation

Answer 1

The function g(x) = -3√(-2x + 4) + 5 represents a transformation of the parent function f(x) = x². The transformations include reflection across the x-axis, vertical stretching by a factor of 3, shifting right by 4 units, and shifting upward by 5 units.

Step-by-step explanation:

The function g(x) = -3√(-2x + 4) + 5 represents a transformation of the parent function f(x) = x². Here are the transformations:

1. The function is reflected across the x-axis, resulting in a negative coefficient in front of the square root.
2. The function is stretched vertically by a factor of 3.
3. The function is shifted to the right by 4 units.
4. The function is shifted upward by 5 units.

Therefore, the function g(x) can be written in function notation as g(x) = -3√(-2(x - 4)) + 5.