Question

reflecting 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 reflected over the $x$-axis and vertically stretched by a factor of 5?
option #1: $f(x) = \frac{-1}{5} \sqrt3{x}$
option #2: $f(x) = -5\sqrt3{x}$
option #3: $f(x) = \sqrt3{\frac{-1}{5}x}$
option #4: $f(x) = \sqrt3{-5x}$
(1 point)

Explanation:

Step1: Recall Transformations

To reflect a function \( f(x) \) over the \( x \)-axis, we multiply the function by \(-1\), so \( f(x) \to -f(x) \). For a vertical stretch by a factor of \( a \), we multiply the function by \( a \), so \( f(x) \to a \cdot f(x) \).

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

First, reflect over the \( x \)-axis: \( -f(x)=-\sqrt[3]{x} \). Then, vertically stretch by a factor of 5: multiply by 5, so \( 5 \cdot (- \sqrt[3]{x})=-5\sqrt[3]{x} \).

Answer:

Option #2: \( f(x) = -5\sqrt[3]{x} \)