Question

Please fill in the table for f(x)=3^x to -f(3x-2)+1
Step 1 Step 2 Step 3 Step 4 Step 5
x _____ _____ ____ _____ ____
1 _____ _____ _____ _____ ____
2 _____ ____ _____ _____ ____
3 ____ ____ _____ ____ ____

Answer 1

To fill in the table for the function \( f(x) = 3^x \) and the transformed function \( -f(3x-2) + 1 \), we can follow these steps carefully.

**Step 1: Calculate \( f(x) \)**

1. \( f(1) = 3^1 = 3 \)
2. \( f(2) = 3^2 = 9 \)
3. \( f(3) = 3^3 = 27 \)

**Step 2: Calculate \( 3x - 2 \)**

1. For \( x=1 \): \( 3(1) - 2 = 1 \)
2. For \( x=2 \): \( 3(2) - 2 = 4 \)
3. For \( x=3 \): \( 3(3) - 2 = 7 \)

**Step 3: Calculate \( f(3x - 2) \)**

Using the results from Step 2, we calculate \( f(3x - 2) \):

1. \( f(1) = 3 \)
2. \( f(4) = 3^4 = 81 \)
3. \( f(7) = 3^7 = 2187 \)

**Step 4: Calculate \( -f(3x - 2) + 1 \)**

Now we take the negative of the results from Step 3 and add one:

1. For \( x=1 \): \( -f(1) + 1 = -3 + 1 = -2 \)
2. For \( x=2 \): \( -f(4) + 1 = -81 + 1 = -80 \)
3. For \( x=3 \): \( -f(7) + 1 = -2187 + 1 = -2186 \)

**Step 5: Fill in the table**

Now we can summarize the values in the table:

| x | f(x) | 3x-2 | f(3x-2) | -f(3x-2) + 1 |
|-------|--------|--------|---------|---------------|
| 1 | 3 | 1 | 3 | -2 |
| 2 | 9 | 4 | 81 | -80 |
| 3 | 27 | 7 | 2187 | -2186 |

With this filled table, you've completed the steps for the transformation \( -f(3x-2) + 1 \) based on the function \( f(x) = 3^x \).