Given the function \( f(x)=x^{3}-1 \), which of the following functions is the new function \( h(x) \) after \( f(x) \) is shifted 10 units up? (1 point) \( h(x)=x^{3}+10 \) \( h(x)=x^{3}-11 \) \( h(x)=x^{3}+9 \) \( h(x)=x^{3}-9 \)

When you shift a function vertically, you add or subtract a constant from the entire function. In this case, since you want to shift the function \( f(x) = x^3 - 1 \) up by 10 units, you would add 10 to the function. This gives us: \[ h(x) = f(x) + 10 = (x^3 - 1) + 10 = x^3 + 9 \] Therefore, the correct option is \( h(x) = x^3 + 9 \). Let's break down why the other options don't work. If you were to choose \( h(x) = x^3 + 10 \), it would mean shifting \( f(x) \) to a new position that isn’t just an upward movement from its original height. Similarly, \( h(x) = x^3 - 11 \) and \( h(x) = x^3 - 9 \) represent downward shifts or incorrect movements of the original curve. Always keep track of your directions when transforming functions!