The problem appears to involve graphs of two functions $F(x)$ (in blue) and $G(x)$ (in red). You're asked to evaluate values related to the functions $P(x) = F(x) + G(x)$ and $Q(x) = F(x) - G(x)$ at certain points.

Specifically, you are required to find the following values:

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

Let's walk through the process:

1. Determine $F(1)$ and $G(1)$:

   • Using the blue graph for $F(x)$ and the red graph for $G(x)$, find the values of each function at $x = 1$.

2. Determine $F(6)$ and $G(6)$:

   • Similarly, find the values of each function at $x = 6$.

3. Compute $P(x)$ and $Q(x)$:

   • $P(x) = F(x) + G(x)$
   • $Q(x) = F(x) - G(x)$

Let me analyze the graphs to extract these values for you.I have opened the image to analyze it. Now, let's extract the relevant values from the graphs.

From the graphs:

1. At $x = 1$:

   • For $F(1)$ (blue graph), find the y-value at $x = 1$.
   • For $G(1)$ (red graph), find the y-value at $x = 1$.

2. At $x = 6$:

   • For $F(6)$ (blue graph), find the y-value at $x = 6$.
   • For $G(6)$ (red graph), find the y-value at $x = 6$.

I'll now read these values from the graph to complete the calculations for $P(1), Q(1), P(6),$ and $Q(6)$.Here are the values directly extracted from the graphs:

At $x = 1$:

• The blue graph $F(x)$ appears to have a y-value of 0 at $x = 1$.
• The red graph $G(x)$ appears to have a y-value of 1 at $x = 1$.

Using these values:

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

At $x = 6$:

• The blue graph $F(x)$ has a y-value of approximately 2 at $x = 6$.
• The red graph $G(x)$ has a y-value of 0 at $x = 6$.

Using these values:

• $P(6) = F(6) + G(6) = 2 + 0 = 2$
• $Q(6) = F(6) - G(6) = 2 - 0 = 2$

Final Answers:

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

Would you like more details, or do you have any questions?

Related Questions:

1. What is the slope of the blue graph $F(x)$ around $x = 1$?
2. Can you find the value of $P(x)$ for another $x$-value from the graphs?
3. How does $G(x)$ behave as $x$ increases beyond 6?
4. Can the behavior of $F(x)$ be classified as exponential, linear, or another type?
5. What would $P(x)$ and $Q(x)$ be if $F(x)$ and $G(x)$ were switched?

Tip:

When reading graphs, zooming in on key points can help ensure accuracy in determining exact values, especially for non-integer coordinates.