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) =1/4x^3 + 1/2

Question

k= 2
k = 4
k = 0
k = 1/4

Answer 1

To identify the factor \( k \) for the vertical compression from the function \( f(x) = x^3 + 2 \) to the function \( g(x) = \frac{1}{4}x^3 + \frac{1}{2} \), we look at the coefficients of the \( x^3 \) terms in both functions.

In the function \( f(x) \): \[ f(x) = x^3 + 2 \] the coefficient of \( x^3 \) is 1.

In the function \( g(x) \): \[ g(x) = \frac{1}{4} x^3 + \frac{1}{2} \] the coefficient of \( x^3 \) is \( \frac{1}{4} \).

The vertical compression factor \( k \) is obtained by comparing these coefficients. The relationship can be expressed as: \[ k = \text{coefficient of } g(x) / \text{coefficient of } f(x) = \frac{1/4}{1} = \frac{1}{4}. \]

Thus, the correct answer is: \[ k = \frac{1}{4}. \]