Question

scaling the cube root function
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given the graph of the function $f(x) = \sqrt3{x}$, what is the new function when horizontally compressed by a factor of 4?
option #1: $f(x) = 4\sqrt3{x}$
option #2: $f(x) = \sqrt3{4x}$
option #3: $f(x) = \frac{1}{4}\sqrt3{x}$
option #4: $f(x) = \sqrt3{\frac{1}{4}x}$
(1 point)

Explanation:

Step1: Recall Horizontal Compression Rule

For a function \( y = f(x) \), a horizontal compression by a factor of \( k \) (where \( k>1 \)) is given by replacing \( x \) with \( kx \) in the function, so the new function is \( y = f(kx) \).

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

Here, the horizontal compression factor is 4. So we replace \( x \) with \( 4x \) in \( f(x)=\sqrt[3]{x} \). Thus, the new function is \( f(x)=\sqrt[3]{4x} \).

Answer:

Option #2: \( \boldsymbol{f(x) = \sqrt[3]{4x}} \)