Question

Complete the table with the order of operations needed to transform f(x) = x
2 + 17 to f(−3x).
Step Order of Operations
1 Option
2 Option
3 Option
Option 1: Raising to the power 2
Option 2: Multiplication
Option 3: Addition

Answer 1

To transform \( f(x) = x^2 + 17 \) to \( f(-3x) \), we can break down the steps involved in this transformation as follows:

**Step Order of Operations:**

1. **Option 2: Multiplication** - Substitute \( -3x \) into the function, which involves multiplying \( x \) by \( -3 \).
2. **Option 1: Raising to the power 2** - Apply the squaring to the result of the multiplication: \( (-3x)^2 \).
3. **Option 3: Addition** - Finally, add 17 to the squared result.

So, the completed table with the order of operations is:

| Step | Order of Operations |
|------|-----------------------------|
| 1 | Option 2: Multiplication |
| 2 | Option 1: Raising to the power 2 |
| 3 | Option 3: Addition |

This correctly reflects the sequence of operations needed to compute \( f(-3x) \).