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Let’s solve the questions step by step based on the given graph of \( g(x) \).

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### (a) \( g(-4) \), \( g(-2) \), \( g(0) \), \( g(2) \), and \( g(4) \):
1. \( g(-4) \): From the graph, when \( x = -4 \), \( g(-4) = 1 \).
2. \( g(-2) \): When \( x = -2 \), \( g(-2) = -3 \).
3. \( g(0) \): When \( x = 0 \), \( g(0) = 0 \).
4. \( g(2) \): When \( x = 2 \), \( g(2) = 3 \).
5. \( g(4) \): When \( x = 4 \), \( g(4) = -1 \).

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### (b) Domain and Range of \( g(x) \):
- **Domain**: The graph extends horizontally from \( x = -4 \) to \( x = 4 \), so \( \text{Domain} = [-4, 4] \).
- **Range**: The vertical extent of the graph is from \( y = -3 \) to \( y = 3 \), so \( \text{Range} = [-3, 3] \).

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### (c) Values of \( x \) for which \( g(x) = 3 \):
From the graph, \( g(x) = 3 \) at \( x = 2 \) and \( x = -3 \).

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### (d) Values of \( x \) for which \( g(x) \leq 0 \):
From the graph, \( g(x) \leq 0 \) for:
- \( x \in [-3, 0] \) (from \( x = -3 \) to \( x = 0 \), including endpoints).

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### (e) Net change in \( g(x) \) between \( x = -1 \) and \( x = 2 \):
- At \( x = -1 \), \( g(-1) = -2 \).
- At \( x = 2 \), \( g(2) = 3 \).
- **Net change**: \( g(2) - g(-1) = 3 - (-2) = 5 \).

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Let me know if you would like a detailed explanation for any part or have further questions. Here are five follow-up questions you might find useful:

1. How can you verify the domain and range from the graph?
2. Why is the net change calculated as \( g(2) - g(-1) \)?
3. Can you determine if \( g(x) \) is a one-to-one function?
4. How would you find where \( g(x) > 0 \) on this graph?
5. What would the slope of the tangent line represent for \( g(x) \) at specific points?

**Tip:** Always observe whether a function is increasing or decreasing between points to better understand its behavior.

Based on the graph of the function g(x) provided, answer the following questions: (a) Find g(-4), g(-2), g(0), g(2), and g(4). (b) Determine the domain and range of g(x). (c) Identify the values of x for which g(x) = 3. (d) Estimate the values of x for which g(x) ≤ 0. (e) Calculate the net change in g(x) between x = -1 and x = 2.

Learn how to analyze the graph of g(x) to determine values, domain, range, inequalities, and net changes. This step-by-step solution explores graph interpretation and mathematical concepts for students in Grades 8-10.

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