Given the function \( f(x)=x^{3}+5 \), which of the following functions is the new function after \( f(x) \) is shifted 3 units up? (1 point) \( h(x)=x^{3}+5 \) \( h(x)=x^{3}+8 \) \( h(x)=x^{3}-5 \) \( h(x)=x^{3}-8 \)

When we shift a function up by a certain number of units, we simply add that number to the entire function. In this case, since we want to shift the function \( f(x) = x^{3} + 5 \) up by 3 units, we calculate: \[ h(x) = f(x) + 3 = (x^{3} + 5) + 3 = x^{3} + 8. \] So the new function would be \( h(x) = x^{3} + 8 \). If you guessed \( h(x) = x^{3} + 8 \), give yourself a high-five! Shifting functions can be quite straightforward once you know the rule! Just remember: up means adding, down means subtracting. Keep those transformations in mind for future math adventures!