The task involves identifying the transformations of a function \( f(x) \) and associating each transformation with a letter. The goal is to solve for the letters and then use them to form a word. Let's break this down step by step.
Step 1: Understand the Problem
The table lists various transformations of the function \( f(x) \). Each transformation corresponds to a letter, and the final goal is to determine the word formed by these letters. The hint at the bottom suggests that the word will be "love," as indicated by \( M + A + T + H = \text{love} \).
Step 2: Identify the Pattern
The transformations are given in a specific order, and each transformation likely corresponds to a specific letter. We need to determine which transformation corresponds to which letter. Typically, such problems involve matching the transformations to a predefined set of letters based on some pattern or rule.
Step 3: Solve for the Letters
Since the problem does not provide explicit values for \( f(x) \), we assume that the transformations are matched to letters in a predetermined way. Let's assign letters to the transformations based on their positions:
1. \( f(x + 8) \)
2. \( f(x) - 5 \)
3. \( f(x - 4) \)
4. \( f(x + 6) + 7 \)
5. \( f(x + 7) - 8 \)
6. \( f(x + 6) + 3 \)
7. \( -f(x - 3) + 4 \)
8. \( -4f(x + 7) \)
9. \( f(-2x) \)
10. \( -f(2x) - 9 \)
11. \( -f\left(\frac{1}{2}x\right) - 2 \)
12. \( -\frac{1}{2}f(x + 4) - 5.5 \)
13. \( 6f\left(\frac{1}{3}(x + 4)\right) + 3 \)
14. \( f(2(x - 6)) + 8 \)
15. \( f\left(-\frac{1}{2}(x - 5)\right) - 9 \)
We need to match these transformations to the letters M, A, T, and H. Without additional context, we can assume that the problem is designed such that the first four transformations correspond to M, A, T, and H.
Step 4: Match Transformations to Letters
Let's assign the first four transformations to the letters M, A, T, and H:
- \( f(x + 8) \) → M
- \( f(x) - 5 \) → A
- \( f(x - 4) \) → T
- \( f(x + 6) + 7 \) → H
Step 5: Form the Word
Using the assigned letters, we have:
- M
- A
- T
- H
The word formed is "MATH".
Final Answer
\[
\boxed{\text{MATH}}
\]
Parent Tip: Review the logic above to help your child master the concept of function transformation worksheet.
