can help prepare you for Precalculus and allow you to compare and contrast between functions. You will create a scrapbook of parent functions and "children". You can use any resources you want to research these functions (e.g., textbook, class notes, internet, other students, teachers) There are functions here that we may not have taught. Do your best to explore them. You do have enough experience with other functions to do this! On each page you should clearly show: A. The graph and formula for the parent function. For each parent function, provide a brief "anecdote" or "interesting fact." B. The graph and formula for the function shifted vertically. C. The graph and formula for the function shifted horizontally.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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**Algebra 2 Functions Scrapbook**

The purpose of this project is to help you summarize properties of functions you have been studying. This can help prepare you for Precalculus and allow you to compare and contrast between functions.

You will create a scrapbook of parent functions and "children." You can use any resources you want to research these functions (e.g., textbook, class notes, internet, other students, teachers) There are functions here that we may not have taught. Do your best to explore them. You do have enough experience with other functions to do this!

On each page you should clearly show:

**A.** The graph and formula for the parent function. For each parent function, provide a brief “anecdote” or “interesting fact.”

**B.** The graph and formula for the function shifted vertically.

**C.** The graph and formula for the function shifted horizontally.

**D.** The graph and formula for the function stretched.

**E.** The graph and formula for the function reflected about the x-axis only.

**F.** Describe the end behavior for each graph.

**G.** Describe the domain, range, increasing, decreasing, and/or constant intervals for each graph.

**H.** Anything else you would like to add to your page. Feel free to get creative, artistic, scientific, humorous, etc!

---

**List of parent functions to be included:**

1. \( f(x) = x \)
2. \( f(x) = |x| \)
3. \( f(x) = x^2 \)
4. \( f(x) = \sqrt{x} \)
5. \( f(x) = x^3 \)
6. \( f(x) = \frac{1}{x} \)
7. \( f(x) = e^x \)
8. \( f(x) = \ln x \)

*Minimum 1 “family” per page*  
(This is meant to be a helpful guideline only.)
Transcribed Image Text:**Algebra 2 Functions Scrapbook** The purpose of this project is to help you summarize properties of functions you have been studying. This can help prepare you for Precalculus and allow you to compare and contrast between functions. You will create a scrapbook of parent functions and "children." You can use any resources you want to research these functions (e.g., textbook, class notes, internet, other students, teachers) There are functions here that we may not have taught. Do your best to explore them. You do have enough experience with other functions to do this! On each page you should clearly show: **A.** The graph and formula for the parent function. For each parent function, provide a brief “anecdote” or “interesting fact.” **B.** The graph and formula for the function shifted vertically. **C.** The graph and formula for the function shifted horizontally. **D.** The graph and formula for the function stretched. **E.** The graph and formula for the function reflected about the x-axis only. **F.** Describe the end behavior for each graph. **G.** Describe the domain, range, increasing, decreasing, and/or constant intervals for each graph. **H.** Anything else you would like to add to your page. Feel free to get creative, artistic, scientific, humorous, etc! --- **List of parent functions to be included:** 1. \( f(x) = x \) 2. \( f(x) = |x| \) 3. \( f(x) = x^2 \) 4. \( f(x) = \sqrt{x} \) 5. \( f(x) = x^3 \) 6. \( f(x) = \frac{1}{x} \) 7. \( f(x) = e^x \) 8. \( f(x) = \ln x \) *Minimum 1 “family” per page* (This is meant to be a helpful guideline only.)
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