Question

shifting the cube root function practice
complete this assessment to review what youve learned. it will not count toward your grade
given the function $f(x) = \sqrt3{x}$, what is the new function when $f(x)$ is shifted down 3 units?
option #1: $f(x) = \sqrt3{x} + 3$
option #2: $f(x) = \sqrt3{x} - 3$
option #3: $f(x) = \sqrt3{x + 3}$
option #4: $f(x) = \sqrt3{x - 3}$
(1 point)

Explanation:

Step1: Recall Vertical Shift Rule

For a function \( y = f(x) \), shifting down \( k \) units (where \( k>0 \)) gives \( y = f(x)-k \).

Step2: Apply the Rule to \( f(x)=\sqrt[3]{x} \)

Here, \( k = 3 \) (shifting down 3 units), so the new function is \( f(x)=\sqrt[3]{x}-3 \).

Answer:

Option #2: \( f(x)=\sqrt[3]{x}-3 \)