The functions f(x) and g(x) are shown on the graph.
f(x)=x^2
what is g(x)?

a. g(x)=(-x)^2+3
b. g(x)=-x^-3
c. g(x)=(-x)^2-3
d. g(x)=-x^2+3

The correct is B)

Step-by-step explanation:

In provided graph f(x) is x² which is equation of parabola

this is shown by blue graph

we need to find the equation of red graph which is denoted by g(x)

It can be seen from graph that g(x) is downward so, in this equation coefficient must be in negative.

In part A)

so,

here is not negative coefficient

In part B)

here is negative coefficient

This shows downward direction of parabola.

and negative 3 shows the shifting of parabola downward by 3 units.

Hence, this condition matches only option B)

In part C)

so,

here is not negative coefficient

In part D)

since, here is negative coefficient  

This shows downward direction of parabola.

and positive 3 shows the shifting of parabola upward by 3 units.

So, the correct is B)

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