Question

If f(x) = x² is reflected over the x-axis and then shifted 2 units down, what is the equation of the new function, g(x)?

1) g(x) = (-x)² + 2
2) g(x) = (-x)² - 2
3) g(x) = -x² + 2
4) g(x) = -x² - 2

Answer 1

The equation of the new function after reflecting f(x) = x² over the x-axis and shifting it downward by 2 units is g(x) = -x² - 2.

Step-by-step explanation:

The student asked: If f(x) = x² is reflected over the x-axis and then shifted 2 units down, what is the equation of the new function, g(x)? To answer this, let's perform the transformations step by step. A reflection over the x-axis means we will multiply the function by -1, so f(x) becomes -x². A downward shift by 2 units means we will subtract 2 from the function, thus transforming -x² into -x² - 2. Therefore, the equation of the new function is g(x) = -x² - 2.