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Let's analyze the given graph of the function \( f \) and answer each question step by step.

### (a) State the value of \( f(-1) \).
To find \( f(-1) \), locate \( x = -1 \) on the graph and find the corresponding \( y \)-value.

**Answer:** \( f(-1) = 0 \).

### (b) Estimate the value of \( f(2) \).
To estimate \( f(2) \), locate \( x = 2 \) on the graph and find the corresponding \( y \)-value.

**Answer:** \( f(2) \approx 1 \).

### (c) For what values of \( x \) is \( f(x) = -2 \)?
Find where the graph intersects the line \( y = -2 \).

**Answer:** The values of \( x \) where \( f(x) = -2 \) are approximately:
- Smaller value: \( x \approx -0.5 \).
- Larger value: \( x \approx 1.5 \).

### (d) Estimate the values of \( x \) such that \( f(x) = 0 \).
Find where the graph intersects the \( x \)-axis.

**Answer:** The values of \( x \) where \( f(x) = 0 \) are:
- Smaller value: \( x = -1 \).
- Larger value: \( x \approx 3 \).

### (e) State the domain and range of \( f \).
**Domain:** The domain is the set of all possible \( x \)-values of the graph.

**Answer:** 
- Domain: \( [-2, 4] \).
- Range: \( [-2, 2] \).

### (f) On what interval is \( f \) increasing?
Identify the intervals where the graph is rising from left to right.

**Answer:** \( f \) is increasing on the interval \( [-2, 0] \) and \( [2, 4] \).

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Do you want more details on any of these answers, or do you have any questions?

### Related Questions:
1. What is the significance of the function's increasing intervals?
2. How do you determine the domain and range of a function from its graph?
3. What does it mean for a function to be increasing or decreasing?
4. How can you identify maximum and minimum points on a graph?
5. What are the intercepts of a function, and how are they useful?

**Tip:** When interpreting graphs, always pay attention to the behavior of the function, including where it crosses the axes and its overall shape!

The graph of a function f is given. Various questions related to analyzing the graph, such as finding f(-1), estimating f(2), and determining intervals for which f(x) = -2, are presented.

Learn how to analyze the graph of a function by estimating values like f(-1) and f(2), identifying where f(x) = -2, and determining the function's domain, range, and intervals of increase. Suitable for students in Grades 7-9.

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