The graph of $g(x)$, shown below, resembles the graph of $f(x)=x^{4}-x^{2}$, but it has been changed somewhat. Which of the following could be the equation of $g(x)$ ? A. $g(x)=x^{4}-x^{2}-2.5$ B. $g(x)=(x-2.5)^{4}-(x-2.5)^{2}$ C. $g(x)=(x+2.5)^{4}-(x+2.5)^{2}$ D. $g(x)=x^{4}-x^{2}+2.5$

Step 1 ：Write the equation of the original function as \(y = x^4 - x^2\).

Step 2 ：The graph of \(g(x)\) is a transformation of the graph of \(f(x)\).

Step 3 ：The transformation could be a vertical shift or a horizontal shift.

Step 4 ：If it is a vertical shift, the equation of \(g(x)\) would be \(y = x^4 - x^2 + c\) or \(y = x^4 - x^2 - c\), where \(c\) is the amount of the shift.

Step 5 ：If it is a horizontal shift, the equation of \(g(x)\) would be \(y = (x-h)^4 - (x-h)^2\) or \(y = (x+h)^4 - (x+h)^2\), where \(h\) is the amount of the shift.

Step 6 ：Comparing the given options with the possible equations of \(g(x)\), we find that option C, \(g(x)=(x+2.5)^{4}-(x+2.5)^{2}\), is a possible equation for \(g(x)\).

Step 7 ：So, the final answer is \(\boxed{\text{(C)}\, g(x)=(x+2.5)^{4}-(x+2.5)^{2}}\).