Question

PLEASE HELP! 50 POINTS

Transform the function f(x)=3^(x+2) so it is translated 6 units left, vertically stretched by a factor of 2, then reflected across the y-axis.

Answer 1

To transform the function \( f(x) = 3^{(x+2)} \) as described:

1. **Translation 6 units left:** Replace \( x \) with \( x + 6 \): \( g(x) = 3^{(x+2)} \) becomes \( g(x) = 3^{(x+2-6)} = 3^{(x-4)} \).

2. **Vertical stretch by a factor of 2:** Multiply the function by 2: \( h(x) = 2 \cdot 3^{(x-4)} \).

3. **Reflection across the y-axis:** Negate the entire function: \( j(x) = -2 \cdot 3^{(x-4)} \).

So, the transformed function is \( j(x) = -2 \cdot 3^{(x-4)} \).

I hope it helps!