The answer is C. g(x) = (x - 2)²
This is because when translating a shape in the x-axis, the signs change. This means that when the graph moves to the right by 2 units, you write it as (x - 2)² instead of (x + 2)². Also, when dealing with translations in the x-axis they must be represented in the brackets, so (x - 2)² as opposed to x² - 2.
You can check that this is true, and also confirm that other answers are false, by substituting in a value of x from the g(x) graph and seeing if it produces the correct y-value. For example, when x = 2, y = 0, so if we substitute x = 2 into each option we get:
A. g(2) = (2 + 2)² = 4² = 16
B. g(2) = (2)² + 2 = 4 + 2 = 6
C. g(2) = (2 - 2)² = 0
D. g(2) = (2)² - 2 = 4 - 2 = 2
I hope this helps! Let me know if you have any questions :)
