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

When you shift a function downwards by a certain number of units, you subtract that number from the function. For \( f(x) = \sqrt[3]{x} \), if you want to shift it down by 3 units, you'll subtract 3 from the original function. Thus, the new function would be \( f(x) = \sqrt[3]{x} - 3 \). This corresponds to Option \#2! Now, let's get a bit nerdy: Did you know that the cube root function results in a shape that is symmetric about the origin? Shifting the graph down will not affect its symmetry; it simply moves the entire function lower on the y-axis while keeping the x-values the same. If you're grappling with transformations of functions, a great way to avoid mistakes is to remember that vertical shifts involve addition or subtraction outside the function. It’s an easy way to keep track of how you’re altering the function. For the cube root, it's all about those y-values!