Question

Complete the table
f(x)=3^x to -f(3x-2)+1

Step1. Step 2. Step3. Step 4. Step 5
1
2
3

Answer 1

To complete the table for the function transformation \( f(x) = 3^x \) reflecting the transformation to \(-f(3x - 2) + 1\), we will analyze the transformations step by step.

1. **Step 1: Evaluate \( f(x) = 3^x \) for \( x = 1, 2, 3 \)**:
- \( f(1) = 3^1 = 3 \)
- \( f(2) = 3^2 = 9 \)
- \( f(3) = 3^3 = 27 \)

2. **Step 2: Evaluate \( f(3x - 2) \)**:
For each \( x \) value:
- For \( x = 1 \): \( f(3(1) - 2) = f(1) = 3 \)
- For \( x = 2 \): \( f(3(2) - 2) = f(4) = 3^4 = 81 \)
- For \( x = 3 \): \( f(3(3) - 2) = f(7) = 3^7 = 2187 \)

3. **Step 3: Evaluate \(-f(3x - 2)\)**:
- For \( x = 1 \): \(-f(3(1) - 2) = -3\)
- For \( x = 2 \): \(-f(3(2) - 2) = -81\)
- For \( x = 3 \): \(-f(3(3) - 2) = -2187\)

4. **Step 4: Evaluate \(-f(3x - 2) + 1\)**:
- For \( x = 1 \): \(-3 + 1 = -2\)
- For \( x = 2 \): \(-81 + 1 = -80\)
- For \( x = 3 \): \(-2187 + 1 = -2186\)

5. **Step 5: Complete the table**: The final values will be filled in as per the transformations applied.

Here is what the completed table looks like:

| Step 1 | Step 2 | Step 3 | Step 4 | Step 5 |
|--------|--------|--------|--------|------------------|
| 3 | 3 | -3 | -2 | -2 |
| 9 | 81 | -81 | -80 | -80 |
| 27 | 2187 | -2187 | -2186 | -2186 |

So, the final column (Step 5) is the outcome of the transformation \( -f(3x - 2) + 1 \) for the given \( x \) values.