https://file.aiquickdraw.com/mathbot/file/1725992281301jtoqdguw.jpg

The problem asks for the graph of \( f + g \), where two functions, \( f(x) \) and \( g(x) \), are shown on the coordinate plane. You are given four possible answer choices (A, B, C, D), and you need to identify which one corresponds to the sum of the functions.

### Steps to solve:
1. **Point-wise Addition**: To obtain the graph of \( f + g \), we need to add the y-values of \( f(x) \) and \( g(x) \) at each x-coordinate.
2. **Evaluate key points**: 
   - For each x-value in the graph, sum the y-values of \( f(x) \) and \( g(x) \).
   - Plot these new points on the graph to form \( f + g \).

### Let's check some key points from the graph:
- At \( x = -4 \), the y-values for \( f(x) \) and \( g(x) \) are both 0, so \( f(-4) + g(-4) = 0 \).
- At \( x = -2 \), \( f(-2) = 1 \) and \( g(-2) = 2 \), so \( f(-2) + g(-2) = 3 \).
- At \( x = 0 \), \( f(0) = 4 \) and \( g(0) = 0 \), so \( f(0) + g(0) = 4 \).
- At \( x = 2 \), \( f(2) = 0 \) and \( g(2) = 2 \), so \( f(2) + g(2) = 2 \).
- At \( x = 4 \), \( f(4) = -3 \) and \( g(4) = 0 \), so \( f(4) + g(4) = -3 \).

### Now compare these values with the graphs in options A, B, C, and D:
- Option **B** shows the correct sums for these points, with:
  - \( f(-4) + g(-4) = 0 \)
  - \( f(-2) + g(-2) = 3 \)
  - \( f(0) + g(0) = 4 \)
  - \( f(2) + g(2) = 2 \)
  - \( f(4) + g(4) = -3 \)

Thus, the correct answer is **B**.

---

Would you like more details on how the addition is performed or have any other questions?

### Related Questions:
1. How do you graph the sum of two functions?
2. What are some other methods for finding the sum of two functions algebraically?
3. How would the graph change if we subtracted \( g(x) \) from \( f(x) \) instead of adding?
4. Can the sum of two functions ever create a discontinuous graph?
5. What happens to the graph of the sum if one of the functions is a constant?

### Tip:
Always check key points, such as intercepts and extrema, when graphing the sum of two functions to verify accuracy.

Which graph represents the sum of the functions f(x) and g(x)?

Learn how to find the graph of the sum of two functions, f(x) and g(x), using point-wise addition. This problem explores graphing techniques and function addition on the coordinate plane, suitable for high school math students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation