Complete the table with the order of operations needed to transform f(x)= x^2 + 17 to f(-3x)

Question

Raising to the power 2
Multiplication
Addition
Step 1
Step2
Step 3

Answer 1

To transform \( f(x) = x^2 + 17 \) to \( f(-3x) \), we can follow these steps:

1. Step 1: Multiplication
   First, we replace \( x \) in the function with \( -3x \). This is a substitution step, but we can consider it similar to multiplication: \[ f(-3x) = (-3x)^2 + 17 \]

2. Step 2: Raising to the power 2
   Next, we need to compute \((-3x)^2\): \[ (-3x)^2 = 9x^2 \] So now we have: \[ f(-3x) = 9x^2 + 17 \]

3. Step 3: Addition
   Finally, we add 17 to the result of the squaring step: \[ f(-3x) = 9x^2 + 17 \]

So the complete table would look like this:

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