Question

Which of the following describes the transformations of g(x)--(2)x+4 -2 from the parent function f(x) = 2*?

Oshift 4 units left, reflect over the x-axis, shift 2 units down
Oshift 4 units left, reflect over the y-axis, shift 2 units down
Oshift 4 units right, reflect over the x-axis, shift 2 units down
Oshift 4 units right, reflect over the y-axis, shift 2 units down

Answer 1

The function g(x) = -2x + 4 - 2 is obtained from the parent function f(x) = 2x through a series of transformations: shift 4 units right, reflect over the y-axis, shift 2 units down.

Step-by-step explanation:

The given function is g(x) = -2x + 4 - 2.

To describe the transformations of g(x) from the parent function f(x) = 2x, we need to identify the modifications applied to f(x).

1. The function has shifted 4 units to the right, as g(x) = f(x - 4).
2. The function has been reflected over the y-axis, as g(x) = -f(x - 4).
3. The function has shifted 2 units down, as g(x) = -f(x - 4) - 2.

Therefore, the correct description of the transformations is shift 4 units right, reflect over the y-axis, shift 2 units down.