To solve this, let’s analyze the graphs of functions $f$ and $g$ provided in the images to find the requested values.

From the Graphs:

The values for each function at the specified points can be observed directly from the graphs.

For $f(1)$:

Locate $x = 1$ on the $f$ graph and identify the corresponding $y$-value.

• $f(1) = 2$

For $g(1)$:

Locate $x = 1$ on the $g$ graph and identify the corresponding $y$-value.

• $g(1) = -1$

For $(f + g)(1)$:

Use the result from $f(1)$ and $g(1)$:

• $f(1) + g(1) = 2 + (-1) = 1$
• $(f + g)(1) = 1$

For $f(2)$:

Locate $x = 2$ on the $f$ graph and identify the corresponding $y$-value.

• $f(2) = 0$

For $g(2)$:

Locate $x = 2$ on the $g$ graph and identify the corresponding $y$-value.

• $g(2) = 3$

For $(f - g)(2)$:

Use the result from $f(2)$ and $g(2)$:

• $f(2) - g(2) = 0 - 3 = -3$
• $(f - g)(2) = -3$

Summary of Answers:

1. (a) $f(1) = 2$
2. (b) $g(1) = -1$
3. (c) $(f + g)(1) = 1$
4. (d) $f(2) = 0$
5. (e) $g(2) = 3$
6. (f) $(f - g)(2) = -3$

Would you like a more detailed explanation of each calculation or assistance with similar problems? Here are some related questions to deepen your understanding:

1. How would you determine $(f + g)(x)$ for other values of $x$?
2. What steps would you follow to calculate $(f \cdot g)(x)$ for given points?
3. How does adding or subtracting function values affect the graph shape?
4. What other transformations can be observed when combining functions?
5. How can you find the domain and range of the combined functions $f + g$ and $f - g$?

Tip: Always double-check function values from graphs by carefully tracing the $y$-coordinates for given $x$-values to avoid errors.