The g(x) will be -x² -2 so option (A) will be correct.
How to plot a graph?
A graph is a diagram that shows the fluctuation of one variable in relation to one or more other variables.
In order to plot the graph, we need to find out y's values corresponding to x's value
The coordinate geometry must then be changed to reflect the values of x and y.
In the figure, it is clear that the graph has shifted 2 units down and the value of the function also gets negative.
In option (A) g(x) = -x² -2 so here the graph has shifted 2 unit down and the value of the function also get negative hence, it will be the correct answer.
For more information about the graph of a function
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