Question

If f(x) = x2 is reflected over the x-axis and then shifted 3 units down, what isthe equation of the new function, g(x)?O A. g(x) = (- x)2 + 3O B. g(x) = -x - 3O C. g(x) = - x2 + 3O D. g(x) = (- x)2 – 3

Answer 1

Hello!

First, let me show you the graph of the function f(x) = x²:

The exercise informs that this graph was shifted 3 units down. It means that the parabola must be the same, it just has to pass the y-axis at point -3, because now it passes when y = 0.

So, as we want that function remains the same and only the interception on the Y-axis to be different, the correct alternative is the letter D. g(x) = (- x)² – 3.

Look at the graph of g(x) = (- x)² – 3 below: