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

Question

𝑓
(
𝑥
)
=
𝑥
3
+
2
to the function f(x)=14x3+12
𝑓
(
𝑥
)
=
1
4
𝑥
3
+
1
2
?(1 point)
Responses

k=2
𝑘
=
2
k equals 2

k=14
𝑘
=
1
4
k equals Start Fraction 1 over 4 End Fraction

k=0
𝑘
=
0
k equals 0

k=4

Answer 1

To find the vertical compression factor \( k \) from the function \( f(x) = x^3 + 2 \) to the function \( f(x) = \frac{1}{4}x^3 + 1 \) (which we can express in standard function form), let's analyze the two functions.

1. Original Function: \[ f(x) = x^3 + 2 \]

2. Transformed Function: \[ g(x) = \frac{1}{4}x^3 + 1 \]

Now, to identify how the transformation affects \( f(x) \):

• The coefficient of \( x^3 \) in the original function is \( 1 \).
• The coefficient of \( x^3 \) in the transformed function \( g(x) \) is \( \frac{1}{4} \).

The vertical compression factor \( k \) can be found as follows:

\[ k = \frac{\text{coefficient of } x^3 \text{ in original}}{\text{coefficient of } x^3 \text{ in transformed}} = \frac{1}{\frac{1}{4}} = 4. \]

Thus, the correct option is:

k=4

So the answer is: k = 4.