Question

scaling the cubic function practice
complete this assessment to review what you’ve learned. it will not count toward your grade.
analyze the graphs and describe the transformation that occurs from $f(x)=x^3 + 5$ to $g(x)=(7x)^3 + 5$.
for the first response, enter 1 for stretch and 2 for compression. if your second response is not a whole number, enter it as a fraction.
(1 point)
the transformation is a horizontal $\square$ by a factor of $\square$.

Explanation:

Step1: Recall Horizontal Stretch/Compression Rules

For a function \( y = f(kx) \), if \( |k|>1 \), it's a horizontal compression by a factor of \( \frac{1}{|k|} \); if \( 0<|k|<1 \), it's a horizontal stretch by a factor of \( \frac{1}{|k|} \). Here, \( f(x)=x^3 + 5 \), \( g(x)=(7x)^3+5=f(7x) \), so \( k = 7 \).

Step2: Determine Transformation Type and Factor

Since \( |k| = 7>1 \), it's a horizontal compression (so enter 2). The factor is \( \frac{1}{7} \) (because the compression factor for \( y = f(kx) \) is \( \frac{1}{k} \) when \( k>0 \)).

Answer:

First box: 2, Second box: \(\frac{1}{7}\)