https://file.aiquickdraw.com/mathbot/file/1726679021988y7kf3e1d.jpg

Looking at the provided graphs for \( f(x) \) and \( g(x) \), let's evaluate the required expressions step by step:

### 1. \( f(1) + g(2) \)
- From the graph of \( f(x) \), at \( x = 1 \), the value of \( f(1) \) is 4.
- From the graph of \( g(x) \), at \( x = 2 \), the value of \( g(2) \) is 5.

Thus, \( f(1) + g(2) = 4 + 5 = 9 \).

### 2. \( f(1) \cdot g(5) \)
- From the graph of \( f(x) \), at \( x = 1 \), the value of \( f(1) \) is 4.
- From the graph of \( g(x) \), at \( x = 5 \), the value of \( g(5) \) is 1.

Thus, \( f(1) \cdot g(5) = 4 \cdot 1 = 4 \).

### 3. \( g(5) - f(4) \)
- From the graph of \( g(x) \), at \( x = 5 \), the value of \( g(5) \) is 1.
- From the graph of \( f(x) \), at \( x = 4 \), the value of \( f(4) \) is 0.

Thus, \( g(5) - f(4) = 1 - 0 = 1 \).

### 4. \( \frac{g(2)}{f(4)} \)
- From the graph of \( g(x) \), at \( x = 2 \), the value of \( g(2) \) is 5.
- From the graph of \( f(x) \), at \( x = 4 \), the value of \( f(4) \) is 0.

Since division by zero is undefined, this expression cannot be evaluated.

Let me know if you'd like further details on any part. Here are five related questions to explore:

1. What is \( f(2) \) and how does it relate to \( g(3) \)?
2. Can you find \( f(3) \cdot g(4) \)?
3. What would \( g(1) + f(2) \) equal based on the graphs?
4. If \( f(x) \) was a linear function, how would you represent its equation?
5. How do you find the inverse of \( g(x) \) based on its graph?

**Tip**: Always check for points where a function touches the x-axis as it might lead to special cases in calculations.

Use the graphs for f(x) and g(x) to evaluate the expressions. Write your answer as a whole number or a reduced fraction.

Learn how to evaluate expressions using function graphs f(x) and g(x). This problem covers interpreting graphs, performing arithmetic operations on functions, and handling cases like division by zero. Suitable for students in Grades 6-8.

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