Question

shifting the cube root function practice
complete this assessment to review what you’ve 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 2 units to the left?
option #1: $f(x) = \sqrt3{x} + 2$
option #2: $f(x) = \sqrt3{x} - 2$
option #3: $f(x + 2) = \sqrt3{x + 2}$
option #4: $f(x - 2) = \sqrt3{x - 2}$
(1 point)

Explanation:

Step1: Recall Horizontal Shift Rule

For a function \( y = f(x) \), a horizontal shift left by \( h \) units (where \( h>0 \)) is given by \( y = f(x + h) \).

Step2: Apply the Rule to Given Function

Here, the original function is \( f(x)=\sqrt[3]{x} \), and we shift it 2 units left. So \( h = 2 \), and the new function is \( f(x + 2)=\sqrt[3]{x + 2} \).

Answer:

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