Question

Vertically compress by a factor of 1/2, then translate the equation 3 units to the right
F(x)=6(x-2)^2

Answer 1

To find the transformed function after applying a vertical compression by a factor of \( \frac{1}{2} \) and then translating the equation 3 units to the right, we can follow these steps:

1. **Vertical Compression**:
The original function is:
\[
F(x) = 6(x - 2)^2
\]
To compress it vertically by a factor of \( \frac{1}{2} \), we multiply the entire function by \( \frac{1}{2} \):
\[
G(x) = \frac{1}{2} \cdot 6(x - 2)^2 = 3(x - 2)^2
\]

2. **Translation**:
To translate the function 3 units to the right, we need to replace \( x \) with \( (x - 3) \) in the function \( G(x) \):
\[
H(x) = G(x - 3) = 3((x - 3) - 2)^2
\]
Simplifying the expression inside the parentheses:
\[
H(x) = 3((x - 5)^2)
\]

Thus, after vertically compressing by a factor of \( \frac{1}{2} \) and translating 3 units to the right, the transformed function is:
\[
H(x) = 3(x - 5)^2
\]