The image shows a question about function transformations. The question is:

Given the parent function f(x) = x, the function g(x) = (x-1)² – 2 is the result of a shift of f(x) by ________.

The possible answers are:

1. 1 unit left and 2 units down

2. 1 unit left and 2 units up

3. 1 unit right and 2 units down

4. 1 unit right and 2 units up

The correct answer is (1), 1 unit left and 2 units down.

The parent function f(x) = x is a straight line that passes through the origin and has a slope of 1. The function g(x) = (x-1)² – 2 is obtained by shifting the function f(x) by 1 unit to the left and 2 units down.

To see this, let’s consider the point (2, 2) on the graph of f(x). This point is also on the graph of g(x), but it is shifted 1 unit to the left and 2 units down. The new coordinates of this point are (1, 0).

Therefore, the function g(x) = (x-1)² – 2 is the result of a shift of f(x) by 1 unit left and 2 units down.

I hope this analysis is helpful. Let me know if you have any other questions.