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Question
Which of the following correctly identifies the factor k for the vertical compression from the function f(x)=x3+2 to the function f(x)=14x3+12 ?(1 point)
Responses

k=2
k equals 2

k=4
k equals 4

k=0
k equals 0

k=14

Answer 1

To determine the factor \( k \) for the vertical compression from the function \( f(x) = x^3 + 2 \) to \( f(x) = 14x^3 + 12 \), we start by analyzing the two functions.

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

To express the transformed function in terms of the original function, we can look at how each term is modified:

- The \( x^3 \) term is multiplied by 14, suggesting a vertical stretch rather than compression.
- The constant term \( 2 \) in the original function translates to \( 12 \) in the transformed function, which shifts the graph vertically but does not affect the factor \( k \).

Regarding the vertical compression factor, it is generally defined when the function is of the form \( k \cdot g(x) \) where \( g(x) \) is the original function.

Here, since the transformation is a vertical stretch (the coefficient of \( x^3 \) increased from \( 1 \) to \( 14 \)), it indicates \( k \) is not a compression factor in this case.

Thus, the correct response for \( k \) identifying the vertical transformation would be:

**k = 14**

Therefore, the correct answer is:
- **k = 14**