https://file.aiquickdraw.com/mathbot/file/17272231396465zzmgn1w.jpg

Let's break down the graph and questions provided in your image step by step.

### (a) Domain and Range:
- **Domain**: The domain represents all possible \( x \)-values for which the function \( f(x) \) is defined. From the graph, we can observe that the function starts at \( x = -4 \) and continues to \( x = 4 \).
  - **Domain**: \( [-4, 4] \)
  
- **Range**: The range is the set of all possible \( y \)-values that the function can take. From the graph, we can see that the lowest point on the \( y \)-axis is \( -2 \), and the highest point is \( 3 \).
  - **Range**: \( [-2, 3] \)

### (b) Find \( f(0) \) and \( f(2) \):
- **\( f(0) \)**: From the graph, when \( x = 0 \), the corresponding \( y \)-value is \( 1 \). Thus, \( f(0) = 1 \).
- **\( f(2) \)**: From the graph, when \( x = 2 \), the corresponding \( y \)-value is \( 3 \). Thus, \( f(2) = 3 \).

### (c) Find the value(s) of \( x \) such that \( f(x) = 2 \):
- To find \( x \) when \( f(x) = 2 \), we locate \( y = 2 \) on the graph. The corresponding \( x \)-value for this point is \( x = 1 \). 
  - So, \( x = 1 \).

### (d) Determine the intervals on which \( f(x) \) is increasing and decreasing:
- **Increasing**: A function is increasing when the graph rises as we move from left to right. From the graph:
  - The function increases from \( x = 0 \) to \( x = 4 \).
  - So, \( f(x) \) is increasing on \( (0, 4] \).
  
- **Decreasing**: A function is decreasing when the graph falls as we move from left to right. From the graph:
  - The function decreases from \( x = -4 \) to \( x = 0 \).
  - So, \( f(x) \) is decreasing on \( [-4, 0] \).

Would you like more details on any of these answers?

Here are five related questions to further your understanding:
1. What is the difference between the domain and the range of a function?
2. How can you determine the increasing and decreasing intervals of a function without a graph?
3. How would the range change if the function were stretched vertically?
4. How do you find \( f(x) \) for non-integer values of \( x \) from the graph?
5. Can a function have more than one interval where it is increasing or decreasing?

**Tip:** Always check the behavior of the function at critical points like where it changes from increasing to decreasing or vice versa.

Consider the graph of y = f(x) below, and answer the following questions:
(a) What is the domain of this function? What is the range?
(b) Find f(0) and f(2).
(c) Find the value(s) of x such that f(x) = 2.
(d) Determine the intervals on which f(x) is increasing and decreasing.

Explore how to find the domain, range, and behavior of a piecewise function by analyzing the graph. Learn how to calculate specific values and determine increasing or decreasing intervals in this problem. Suitable for students in Grades 9-11.

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