Question

Which equation for g(x) represents the transformation of f(x) given that f(x) =x^2

g(x) = f(x) shifted right 2 units
Help!!

Answer 1

g(x) = (x - 2)²

Explanation:

If we want to shift a function to the right, we subtract the number we are asked to move to the right inside the function's argument:

⇒ To shift f(x) b units to right → f(x - b)

Similarly, in function notation, if we want to shift a function to the left, we add the number we are asked to move to the left inside the function's argument:

⇒ To shift f(x) b units to left → f(x + b)

Given function f(x) = x²

Shift 2 units to the right: f(x - 2) = (x - 2)²

Therefore, g(x) = (x - 2)²

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Additional info:

g(x) = (x - 2)²

= (x - 2)(x - 2)

= x² - 4x + 4