Which of the following correctly identifies the factor k for the vertical compression from the function f(x)=x3+2

Question

to the function f(x)=14x3+12
?(1 point)
Responses

k=4
k equals 4

k=0
k equals 0

k=2
k equals 2

k=14

Answer 1

To identify the factor \( k \) for the vertical transformation from the function \( f(x) = x^3 + 2 \) to the function \( f(x) = 14x^3 + 12 \), we need to analyze the vertical scaling in the terms involving \( x^3 \).

1. The original function is \( f(x) = x^3 + 2 \).
2. The transformed function is \( f(x) = 14x^3 + 12 \).

The vertical transformation can be expressed in terms of a factor \( k \): \[ f(x) = k \cdot g(x) + C \] Where \( g(x) \) is the original function and \( C \) is a constant.

From the \( x^3 \) term:

• The original coefficient is \( 1 \) (as \( x^3 \) can be seen as \( 1 \cdot x^3 \)).
• The modified coefficient is \( 14 \).

This indicates a vertical stretch because the coefficient increases.

The factor \( k \) is determined by how much the coefficient of the \( x^3 \) term is multiplied to obtain the transformation. Therefore, \[ k = 14. \]

Thus, the correct response identifying the factor \( k \) for the vertical compression (or in this case, vertical stretch) is:

• \( k = 14 \).