Determine the equation

Option A - .

Step-by-step explanation:

Given : The graph of and the graph of F(x) which is changed somewhat.

To find : The equation of graph F(x)

Solution :

Since, According to the given statement we get F(x)  by doing some changes in G(x).

In the graph, it seems that F(x) is shifting vertically downward by 4 unit than G(x).

When the function is shifted to vertically downward then

i.e, f(x) → f(x)-b ⇒  f(x) shifted downward by b unit.

We also see that the graph of F(x) is reflected over x-axis.

Reflection over x-axis meas y=-x i.e, signs are changed.

So,

Therefore, Option A is correct.

The graph is .