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The functions f(x) and g(x) are shown on the graph.F(x)=x^2What is g(x)?A. g(x)= -x^2+3B. g(x)=(-x)^2-3C. g(x)=(-x)^2+3D.g(x)= -x^2-3

The Functions Fx And Gx Are Shown On The GraphFxx2What Is GxA Gx X23B Gxx23C Gxx23Dgx X23 class=

Sagot :

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.

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