https://file.aiquickdraw.com/mathbot/file/1726621311912u9iq2ucs.jpg

Let's break down and solve the questions based on the graph and the provided instructions.

### 1. Graph Analysis
The graph of \( f(x) \) is a piecewise linear function. From the visual representation, we can observe the behavior of the function at key points:

- The function is symmetric and forms a "V" shape.
- \( f(x) \) appears to have the following critical points:
  - \( f(-4) = 0 \)
  - \( f(-2) = -2 \)
  - \( f(0) = 0 \)
  - \( f(2) = 2 \)
  - \( f(4) = 0 \)
  
The graph appears to consist of straight lines connecting these points.

### Problem Breakdown:

#### (a) **Find \( f(-2) \)**:
By observing the graph, at \( x = -2 \), the function has a value of \( f(-2) = -2 \).

#### (b) **Given \( g(x) = f(x) + 2 \), find \( g(0) \)**:
- We already know that \( f(0) = 0 \).
- Therefore, \( g(0) = f(0) + 2 = 0 + 2 = 2 \).

#### (c) **Sketch the graph of \( g(x) \)**:
- The graph of \( g(x) = f(x) + 2 \) is simply a vertical translation of the graph of \( f(x) \) by 2 units upward. 
- All points on the graph of \( f(x) \) are moved 2 units higher. For example:
  - \( f(-4) = 0 \), so \( g(-4) = 2 \)
  - \( f(-2) = -2 \), so \( g(-2) = 0 \)
  - \( f(0) = 0 \), so \( g(0) = 2 \)
  - \( f(2) = 2 \), so \( g(2) = 4 \)
  - \( f(4) = 0 \), so \( g(4) = 2 \)

The new graph of \( g(x) \) will be an identical shape to \( f(x) \), just shifted upward by 2 units.

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Do you want more details or explanations for any part of this solution? 

Here are five related questions to explore this further:

1. How would the graph of \( g(x) = f(x) - 2 \) look like?
2. What is the slope of the line segments in the graph of \( f(x) \)?
3. Can you express \( f(x) \) as a piecewise function based on the graph?
4. How would the domain and range of \( g(x) \) differ from those of \( f(x) \)?
5. What happens to the graph if \( g(x) = 2f(x) \)?

**Tip**: When dealing with transformations of graphs, always look for shifts, stretches, and reflections to understand how the shape changes.

Diberikan grafik fungsi f(x). Tentukan nilai dari f(-2), jika g(x) = f(x) + 2 tentukan nilai dari g(0), dan sketsa grafik dari g(x).

Solve the problem of finding f(-2) and g(0) based on a piecewise function f(x), and sketch the graph of g(x) = f(x) + 2. Learn about vertical translations and analyzing function graphs.

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