Question

How would you describe the difference between the graphs of f(x) = 2x² and

g(x) = -2x²?
O A. g(x) is a reflection of f(x) over the line y = x.
B. g(x) is a reflection of f(x) over the line y = -1.
C. g(x) is a reflection of f(x) over the y-axis.
D. g(x) is a reflection of f(x) over the x-axis.

Answer 1

D. g(x) is a reflection of f(x) over the x-axis.

Explanation:

So when you have the equation:
`-2x^2` it's just negating the value of f(x), which is
`2x^2` and since f(x) represents the y-value, you're negating the y-value and the x-value is unchanged. So each point on f(x) was originally: (x, f(x)) and now it's (x, -f(x)). Since the y-value is changing, it's going to be reflecting across the x-axis. So g(x) is a reflection of f(x) over the x-axis.