Question

Which translation maps the graph of the function (f(x) = x²) onto the function (g(x) = x² - 6x + 6)?

a) Left 3 units, down 3 units
b) Right 3 units, down 3 units
c) Left 6 units, down 1 unit
d) Right 6 units, down 1 unit

Answer 1

The function g(x) = x² - 6x + 6 is derived from the function f(x) = x² by completing the square, which shows that f(x) has been translated to the right by 3 units and down by 3 units to obtain g(x).

Step-by-step explanation:

To determine which translation maps the graph of the function f(x) = x² onto the function g(x) = x² - 6x + 6, we can complete the square for the function g(x). Completing the square involves finding a number to add and subtract that forms a perfect square trinomial. The function g(x) can be rewritten as g(x) = (x-3)² + 3. This shows that the graph of f(x) = x² is translated to the right by 3 units and down by 3 units to get the graph of g(x). Therefore, the correct answer is b) Right 3 units, down 3 units.