https://file.aiquickdraw.com/mathbot/file/1726678643828kk6f1tsd.jpg

Let's work through the questions visible in your image, which involves the functions \( f(x) \) and \( g(x) \) displayed as graphs. 

### Step-by-step approach:

1. **For \( f(1) + g(2) \):**
   - \( f(1) \): From the graph of \( f(x) \), locate \( x = 1 \). The corresponding \( y \)-value appears to be **4**.
   - \( g(2) \): From the graph of \( g(x) \), locate \( x = 2 \). The corresponding \( y \)-value appears to be **5**.
   - \( f(1) + g(2) = 4 + 5 = 9 \).

2. **For \( f(1) \cdot g(5) \):**
   - \( f(1) \): As calculated before, \( f(1) = 4 \).
   - \( g(5) \): From the graph of \( g(x) \), locate \( x = 5 \). The corresponding \( y \)-value is **2**.
   - \( f(1) \cdot g(5) = 4 \cdot 2 = 8 \).

3. **For \( g(5) - f(4) \):**
   - \( g(5) \): From the graph of \( g(x) \), \( g(5) = 2 \).
   - \( f(4) \): From the graph of \( f(x) \), locate \( x = 4 \). The corresponding \( y \)-value is **3**.
   - \( g(5) - f(4) = 2 - 3 = -1 \).

4. **For \( \frac{g(2)}{f(4)} \):**
   - \( g(2) \): From the graph of \( g(x) \), \( g(2) = 5 \) (as previously calculated).
   - \( f(4) \): From the graph of \( f(x) \), \( f(4) = 3 \) (as previously calculated).
   - \( \frac{g(2)}{f(4)} = \frac{5}{3} \).

### Final answers:
- \( f(1) + g(2) = 9 \)
- \( f(1) \cdot g(5) = 8 \)
- \( g(5) - f(4) = -1 \)
- \( \frac{g(2)}{f(4)} = \frac{5}{3} \)

Would you like further details or clarifications?

Here are five related questions to deepen your understanding:
1. How do you interpret the operations on functions graphically?
2. What happens when the value of \( f(x) \) or \( g(x) \) is zero?
3. How would the result change if you had \( f(x) - g(x) \) instead of \( f(x) + g(x) \)?
4. What are the practical applications of performing operations like \( f(x) \cdot g(x) \)?
5. Can function operations like division always be performed, or are there restrictions?

**Tip:** When multiplying or dividing functions, be cautious of values that make one of the functions zero, as they could impact the solution.

Use the graphs for f(x) and g(x) to evaluate the expressions: f(1) + g(2), f(1) * g(5), g(5) - f(4), and g(2) / f(4).

Learn how to evaluate expressions involving function operations using graphical analysis. This example covers evaluating expressions like f(1) + g(2), f(1) * g(5), g(5) - f(4), and g(2) / f(4) by interpreting function graphs. Suitable for students in Grades 9-11.

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