On observation of the graphs of the two functions, we can see that f(x) has undergone some transformation to give g(x).
The original function is given as
[tex]f(x)=x^2[/tex]
The function is reflected over the x-axis.
The rule for the reflection over the x-axis is given as
[tex]f(x)\to-f(x)[/tex]
Applying this to the function, we have the new function to be
[tex]-x^2[/tex]
The graph is also shifted downwards by 3 units.
This shift can be represented as
[tex]f(x)\to f(x)-3[/tex]
Applying this to our function, we have the new function, g(x), to be
[tex]g(x)=-x^2-3[/tex]
The correct option is OPTION D.
