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

A. g(x) is a reflection of f(x) over the line y=-1.

B. g(x) is a reflection of f(x) over the line y = x.

C. g(x) is a reflection of f(x) over the yaxis.

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

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

Step-by-step explanation:

Given

f(x) = 2x²

g(x) = -2x²

Required

Determine the difference between f(x) and g(x)

Start by expanding g(x)

g(x) = -2x²

g(x) = -1 * 2x²

Substitute 2x² for f(x)

g(x) = -1 * f(x)

g(x) = -f(x)

Using the format (x,y):

Take for instance x = 2

f(x) = 2x² = 2 * 2² = 2 * 4 = 8

This means (x,y) = (2,8)

g(x) = -f(x)= -8

This means that (2,-8)

Notice that only the y value changed in both cases from 8 to -8

From the above expression, g(x) = -f(x) and illustration of when x = 2

This implies that g(x) is a reflection of f(x) along the x axis..

From the list of given options, the correct answer is D.