https://file.aiquickdraw.com/mathbot/file/1726621931720cuc4hfgj.jpg

The problem you provided contains a graph of the function \( f(x) \) and has several questions related to it. Here's a breakdown of the problem and its questions:

### Graph Interpretation:
The function \( f(x) \) appears to be a piecewise linear function, with the graph forming peaks and valleys. Here are some key points visible from the graph:

1. The function has a peak at \( x = -2 \) where \( f(-2) = 3 \).
2. It decreases until \( x = 0 \), where \( f(0) = -2 \).
3. Then it increases to a peak at \( x = 2 \), where \( f(2) = 3 \).
4. Finally, it decreases again beyond \( x = 2 \).

Now, let’s address each question.

### (a) Determine the value of \( f(-2) \):
From the graph, we can see that at \( x = -2 \), the function reaches its peak, so:
\[
f(-2) = 3
\]

### (b) If \( g(x) = f(x) + 2 \), determine the value of \( g(0) \):
We know that \( f(0) = -2 \) from the graph. Using the given function \( g(x) = f(x) + 2 \), we substitute \( x = 0 \):
\[
g(0) = f(0) + 2 = -2 + 2 = 0
\]

### (c) Sketch the graph of \( g(x) \):
To sketch the graph of \( g(x) = f(x) + 2 \), we shift the entire graph of \( f(x) \) upward by 2 units. This means:

- The peak at \( f(-2) = 3 \) will now be at \( g(-2) = 5 \).
- The valley at \( f(0) = -2 \) will move to \( g(0) = 0 \).
- The peak at \( f(2) = 3 \) will shift to \( g(2) = 5 \).

So, the graph of \( g(x) \) will have the same shape as \( f(x) \), just shifted vertically by 2 units.

---

Would you like more details on any of the answers or further clarification?

Here are 5 questions for further exploration:
1. How would you determine the slope of each segment in the piecewise function \( f(x) \)?
2. What changes to the graph would occur if \( g(x) = f(x) - 3 \)?
3. Can you write the piecewise linear equations for each segment of \( f(x) \)?
4. How does the vertical shift affect the zeros of the function \( g(x) \)?
5. Could you find the domain and range of both \( f(x) \) and \( g(x) \)?

**Tip:** When shifting a graph vertically by \( k \), each point \( (x, y) \) on the graph moves to \( (x, y+k) \).

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

Learn how to solve a graph-based function problem, including finding f(-2), determining g(0) with a vertical shift, and sketching the graph of g(x) = f(x) + 2. This problem covers graphing piecewise functions and function transformations. Suitable for high school students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation