Which of the following functions undergoes a vertical compression? Option \#1: \( f(x)=5 x^{3} \) Option \#2: \( f(x)=-\frac{3}{2} x^{3} \) Option \#3: \( f(x)=-\frac{5}{7} x^{3} \) (1 point)
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A vertical compression occurs when a function is multiplied by a constant that is between 0 and 1. In this case, Option #3, \( f(x)=-\frac{5}{7} x^{3} \), has a coefficient of \(-\frac{5}{7}\), which is less than 1 in absolute value, indicating that the function is compressed vertically compared to the original cubic function. Option #1 and Option #2 have coefficients that do not qualify for vertical compression. Option #1 has a coefficient of 5, which suggests vertical stretching, and Option #2 has \(-\frac{3}{2}\), which also indicates vertical stretching, even though it's negative.