1. f(x) = -x+2
@ Identity the function family
2. f(x) = x2-2
@List all
transformations
3. 9 (х) =2x-2
4. h(x) = 2.21x+ 2)?

Let's go through each function one by one.

### 1. \( f(x) = -x + 2 \)
**Identify the function family:**
- This is a **linear function** because it is of the form \( f(x) = mx + b \), where \( m = -1 \) and \( b = 2 \).

### 2. \( f(x) = x^2 - 2 \)
**List all transformations:**
- The base function is \( f(x) = x^2 \), which is a **quadratic function**.
- **Transformation:**
  - **Vertical shift down by 2 units**: The "-2" at the end shifts the graph of \( x^2 \) down by 2 units.

### 3. \( g(x) = 2x - 2 \)
This is another **linear function**. It is of the form \( g(x) = mx + b \), where \( m = 2 \) and \( b = -2 \).

### 4. \( h(x) = 2.21x + 2 \)
This function is also **linear** because it can be written as \( h(x) = 2.21x + 2 \), where the slope \( m = 2.21 \) and the y-intercept \( b = 2 \).

Would you like more details or have any questions?

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Here are 5 related questions that expand on this information:

1. What is the slope and y-intercept of the function \( f(x) = -x + 2 \)?
2. How does the graph of \( f(x) = x^2 - 2 \) compare to the graph of \( f(x) = x^2 \)?
3. What is the significance of the slope in the linear function \( g(x) = 2x - 2 \)?
4. How would the graph of \( h(x) = 2.21x + 2 \) change if the slope were negative?
5. What are the similarities and differences between the functions \( g(x) = 2x - 2 \) and \( h(x) = 2.21x + 2 \)?

**Tip:** Understanding the general form of a function helps in quickly identifying its family and transformations.

Explore examples of linear and quadratic functions, including transformations and key characteristics. Learn about linear functions like f(x) = -x + 2 and g(x) = 2x - 2, as well as quadratic functions like f(x) = x^2 - 2. Understand their graphical representations and how to identify transformations. Suitable for high school students.

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