which of the following correctly identifies the factor k for the vertical compression from the function f (x) = x^3 + 2 to the function f (x) = 1/4 x^3 + 1/2

Answer 1

To determine the factor \( k \) for the vertical compression from the function \( f(x) = x^3 + 2 \) to the function \( f(x) = \frac{1}{4}x^3 + \frac{1}{2} \), we can focus on the leading term of each function, as the vertical compression is influenced by this term.

1. The leading term of the original function is \( x^3 \).
2. The leading term of the transformed function is \( \frac{1}{4}x^3 \).

To find the vertical compression factor \( k \):

\[ k = \text{leading coefficient of the new function} \div \text{leading coefficient of the original function} = \frac{\frac{1}{4}}{1} = \frac{1}{4} \]

Thus, the factor \( k \) for the vertical compression is \( \frac{1}{4} \).

So, the correct answer is \( k = \frac{1}{4} \).