The point of inflection of the cubic function \( f(x) \), is \( (-5,0) \). What is the equation of the new function \( h(x) \) that is obtained by shifting \( f(x) 6 \) units to the right? (1 point) \( h(x)=(x-11)^{3} \) \( h(x)=(x-1)^{3} \) \( h(x)=(x+11)^{3} \) \( h(x)=(x+1)^{3} \)

When a cubic function has a point of inflection at \((-5, 0)\), the function can be expressed in the form \( f(x) \). To shift this function 6 units to the right, you simply replace \(x\) with \(x - 6\). Thus, the new function becomes \( h(x) = f(x - 6) \). Given the point of inflection of \( f(x) \), moving it 6 units to the right results in a new point of inflection at \((-5 + 6, 0) = (1, 0)\). Therefore, \( h(x) \) can be expressed as \( h(x) = (x - 1)^3 \), making the correct choice \( h(x) = (x - 1)^3 \).