Test Review: Transformations and Parent Functions

Welcome to review week! Today and tomorrow, we are focusing on consolidating everything we have learned this cycle. Your test is scheduled for Wednesday.

This assessment will cover the fundamental building blocks of functions. To ensure you are fully prepared, focus your study time on the following key areas:

  • Vocabulary: Understand terms like domain, range, intercept, and asymptote.
  • Transformations: Be able to identify and apply:
    • Translations (Vertical and Horizontal shifts)
    • Reflections (Over the $x$-axis or $y$-axis)
    • Vertical Stretching and Compressing
  • Parent Functions: Recognize the shapes and equations of basic functions (Linear, Quadratic, Absolute Value, Cubic, etc.).
  • Application: Transform specific points given a rule and use parent functions to describe changes in a graph.
  • Analysis: State the Domain and Range using interval notation or inequality notation from a graph.

Key Concepts Recap

Remember the general form for transforming a function $f(x)$:

$$g(x) = a \cdot f(x - h) + k$$

Here is a quick cheat sheet for what each variable does:

  • $h$ (Horizontal Shift): Moves the graph left or right. Remember, it is usually the opposite of what you see inside the parenthesis. If you have $(x-3)$, you move right 3 units.
  • $k$ (Vertical Shift): Moves the graph up or down. If you have $+4$, you move up 4 units.
  • $a$ (Stretch/Compress/Reflect):
    • If $a$ is negative, the graph reflects across the $x$-axis.
    • If $|a| > 1$, it is a vertical stretch (narrower).
    • If $0 < |a| < 1$, it is a vertical compression (wider).

Study Resources

Below are several resources to help you practice. Use the videos to review concepts you are struggling with and the practice problems to test your speed and accuracy.

Online Practice:

Textbook Resources (Holt Online):

  • Section 1-1: Practice Quiz & Homework Help (Videos/Solutions)
  • Section 1-2: Practice Quiz & Homework Help (Videos/Solutions)

Assignments & Discussion

Homework (Due Tomorrow Night):
Please answer the following three questions:

  1. Which specific resource listed above was the most helpful for your studying?
  2. What other resource did you find on your own to study?
  3. What grade do you predict you will earn on the test?

Discussion Board (3 Points):
Find a resource (video, website, or game) that you used to study and share it with the class. Do not just post the link. Please explain what the link covers and specifically how it helped you understand a concept better.

Good luck studying! Let's finish this cycle strong.