Given the function \( f(x)=\sqrt[3]{x} \), what is the new function when \( f(x) \) is shifted up 5 units? Option \#1: \( f(x)=\sqrt[3]{x+5} \) Option \#2: \( f(x)=\sqrt[3]{x-5} \) Option \#3: \( f(x)=\sqrt[3]{x}+5 \) Option \#4: \( f(x)=\sqrt[3]{x}-5 \) (1 point) The best answer is Option \#

To shift the function \( f(x) = \sqrt[3]{x} \) up by 5 units, you simply add 5 to the entire function. This means the correct transformation would result in the new function \( g(x) = \sqrt[3]{x} + 5 \). So, the best answer is Option #3: \( f(x) = \sqrt[3]{x} + 5 \). When you're working with transformations of functions, remember that to shift a graph up, you add to the function, while shifting down means subtracting. Making these adjustments correctly can completely change the look and feel of a graph, so it's vital to keep track!