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The uploaded image contains problems that involve sketching and describing transformations of functions on graphs. Here’s a breakdown of each task from the image:

### Problem Descriptions:

1. **Task 3: Skizzieren Sie die Graphen der Funktionen in ein gemeinsames Koordinatensystem.**
   - This translates to "Sketch the graphs of the functions in a common coordinate system."
   - Functions provided:
     - a) \( f(x) = x^2 \)
     - \( g(x) = x^2 - 15 \)
     - \( h(x) = (x + 3)^2 \)
   
   - b) Functions:
     - \( f(x) = x^2 \)
     - \( g(x) = x^2 + 1 \)
     - \( h(x) = (x - 3)^2 \)
   
   - c) Functions:
     - \( f(x) = x^3 \)
     - \( g(x) = x^3 - 2 \)
     - \( h(x) = (x - 3)^3 \)

   - d) Functions:
     - \( f(x) = x^3 \)
     - \( g(x) = \frac{1}{2}x^3 - 3 \)
     - \( h(x) = -\frac{1}{2}x^3 \)

2. **Task 4: Beschreiben Sie, wie man den Graphen der Funktionen erhält und geben Sie einen Funktionsterm an.**
   - This translates to "Describe how to obtain the graph of the functions and provide the function equation."
   - The task shows transformations involving shifting, stretching, compressing, and reflecting functions.

3. **Task 5: Skizzieren Sie die Graphen der Funktionen in ein gemeinsames Koordinatensystem.**
   - This translates similarly to Task 3, focusing on sketching and comparing graphs of given functions.

### Problem Analysis and Approach:

- The questions require you to understand function transformations such as shifts (horizontal and vertical), stretches, compressions, and reflections.
- When sketching these functions, the primary approach is:
  - Identify the parent function (e.g., \( x^2 \) or \( x^3 \)).
  - Apply the transformations sequentially:
    - Horizontal shifts: Adjust \( x \) inside the function (e.g., \( (x - 3)^2 \) shifts 3 units right).
    - Vertical shifts: Add or subtract outside the function (e.g., \( x^2 + 1 \) shifts 1 unit up).
    - Reflections: Multiply by negative values (e.g., \( -\frac{1}{2}x^3 \)).
    - Stretches/compressions: Multiply by constants (e.g., \( \frac{1}{2}x^3 \)).

Would you like me to detail how to sketch each graph or explain specific transformations from these problems? Here are some questions related to the tasks:

1. How do you determine vertical and horizontal shifts in a graph?
2. What is the effect of reflecting a function across the x-axis or y-axis?
3. How do stretching and compressing affect the appearance of a graph?
4. How can you identify the parent function of a transformed function?
5. What are the key points to plot when sketching transformed functions?

**Tip:** When sketching transformations, start by drawing the basic parent function, then apply transformations step-by-step to understand how the graph changes.

Skizzieren Sie die Graphen der Funktionen in ein gemeinsames Koordinatensystem. Beschreiben Sie, wie man den Graphen erhält und geben Sie einen Funktionsterm an.

Learn how to sketch graphs of quadratic and cubic functions, including transformations like horizontal shifts, vertical shifts, and reflections. This task involves functions such as f(x) = x^2, g(x) = x^2 - 15, and h(x) = (x + 3)^2. Suitable for students in Grades 10-12.

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