The problem in the image asks us to analyze graphs of two functions, $F(x)$ (in blue) and $G(x)$ (in red), and then to answer some questions based on combined operations involving $F(x)$ and $G(x)$. The questions involve evaluating new functions defined in terms of $F(x)$ and $G(x)$. Let's proceed step by step to solve this.

The given graphs and questions are as follows:

• Let $P(x) = F(x) + G(x)$
• Let $Q(x) = F(x) \cdot G(x)$

We need to answer the following:

1. $P(1)$
2. $Q(1)$
3. $P(6)$
4. $Q(6)$

Let’s determine the values from the graphs.

Step-by-Step Analysis

1. Identify $F(x)$ and $G(x)$ Values from Graphs:
   • Blue graph: $F(x)$
   • Red graph: $G(x)$

Finding Required Values:

1. $P(1) = F(1) + G(1)$:

   • From the blue graph, find $F(1)$.
   • From the red graph, find $G(1)$.
   • Add these values.

2. $Q(1) = F(1) \times G(1)$:

   • Use the values of $F(1)$ and $G(1)$.
   • Multiply these values.

3. $P(6) = F(6) + G(6)$:

   • From the blue graph, find $F(6)$.
   • From the red graph, find $G(6)$.
   • Add these values.

4. $Q(6) = F(6) \times G(6)$:

   • Use the values of $F(6)$ and $G(6)$.
   • Multiply these values.

Reading Graphs:

To provide accurate answers, I'll read the graph points:

• Blue graph (top) for $F(x)$
• Red graph (bottom) for $G(x)$

Let me analyze the image and extract these values.

Determining Graph Values:

• $F(1)$ (Blue graph):

  • It looks like $F(1) \approx -1$.

• $G(1)$ (Red graph):

  • It appears that $G(1) \approx 1$.

So:

• $P(1) = F(1) + G(1) = -1 + 1 = 0$
• $Q(1) = F(1) \times G(1) = (-1) \times 1 = -1$

Now for $x = 6$:

• $F(6)$ (Blue graph):

  • It seems $F(6) \approx -1.5$.

• $G(6)$ (Red graph):

  • It seems $G(6) \approx 0.5$.

So:

• $P(6) = F(6) + G(6) = -1.5 + 0.5 = -1$
• $Q(6) = F(6) \times G(6) = (-1.5) \times 0.5 = -0.75$

Final Answers:

1. $P(1) = 0$
2. $Q(1) = -1$
3. $P(6) = -1$
4. $Q(6) = -0.75$

Would you like more details or have any questions about the steps? Here are some further questions that might be useful for practice:

1. What is $P(x)$ for other values of $x$, like $x = 2$ or $x = 4$?
2. How would $Q(x)$ behave if either $F(x)$ or $G(x)$ were zero?
3. Could you graph $P(x)$ and $Q(x)$ based on these two graphs?
4. What would happen to $P(x)$ and $Q(x)$ if $F(x)$ and $G(x)$ were shifted vertically?
5. How can we interpret the behavior of $P(x)$ when $F(x)$ and $G(x)$ have different signs?

Tip: When analyzing graphs, always identify key points and their respective function values to simplify calculations involving combinations of functions.