Question

scaling 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 vertically stretched by a factor of 4?
option #1: $f(x) = \sqrt3{x + 4}$
option #2: $f(x) = \sqrt3{x} + 4$
option #3: $f(x) = 4\sqrt3{x}$
option #4: $f(x) = \sqrt3{4x}$
(1 point)

Explanation:

Step1: Recall Vertical Stretch Rule

For a function \( y = f(x) \), a vertical stretch by a factor of \( a \) (where \( a>1 \)) transforms the function to \( y = a \cdot f(x) \).

Step2: Apply the Rule to Given Function

Given \( f(x)=\sqrt[3]{x} \), a vertical stretch by factor 4 means we multiply \( f(x) \) by 4. So the new function is \( f(x) = 4\sqrt[3]{x} \).

Answer:

Option #3: \( f(x) = 4\sqrt[3]{x} \)