Question

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