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Let's evaluate the functions \( f(x) \) and \( g(x) \) based on the provided graphs for the exercises 51-54.

### From the graphs:
- The graph of \( f(x) \) is a "V" shape:
  - \( f(1) = 2 \)
  - \( f(2) = 0 \)
  - \( f(3) = 2 \)
  - \( f(4) = 4 \)

- The graph of \( g(x) \) is a straight line with a negative slope:
  - \( g(1) = 4 \)
  - \( g(2) = 3 \)
  - \( g(3) = 2 \)
  - \( g(4) = 1 \)

### Let's evaluate each question:

#### 51. (a) \( (f + g)(3) \)
\[
(f + g)(3) = f(3) + g(3) = 2 + 2 = 4
\]

(b) \( \left(\frac{f}{g}\right)(2) \)
\[
\left(\frac{f}{g}\right)(2) = \frac{f(2)}{g(2)} = \frac{0}{3} = 0
\]

#### 52. (a) \( (f - g)(1) \)
\[
(f - g)(1) = f(1) - g(1) = 2 - 4 = -2
\]

(b) \( (fg)(4) \)
\[
(fg)(4) = f(4) \cdot g(4) = 4 \cdot 1 = 4
\]

#### 53. (a) \( (f \circ g)(2) \)
\[
(f \circ g)(2) = f(g(2)) = f(3) = 2
\]

(b) \( (g \circ f)(2) \)
\[
(g \circ f)(2) = g(f(2)) = g(0)
\]
\( g(0) \) is not defined on the graph, so this is undefined.

#### 54. (a) \( (f \circ g)(1) \)
\[
(f \circ g)(1) = f(g(1)) = f(4) = 4
\]

(b) \( (g \circ f)(3) \)
\[
(g \circ f)(3) = g(f(3)) = g(2) = 3
\]

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Would you like further details on any of these computations?

### Related Questions:
1. What is the domain and range of the functions \( f(x) \) and \( g(x) \)?
2. How would the composition \( (f \circ g)(x) \) be generally evaluated for any \( x \)?
3. Can \( g \circ f(x) \) have undefined values, and why?
4. What happens when you add, subtract, or multiply two functions graphically?
5. How can you use these graphs to approximate the derivative of \( f(x) \) or \( g(x) \)?

### Tip:
When composing two functions, always evaluate the inner function first and ensure that the result falls within the domain of the outer function.

Evaluate the functions f(x) and g(x) based on the graphs provided for exercises 51-54.

Explore exercises involving function operations such as addition, subtraction, multiplication, and division, along with function composition using the graphs of f(x) and g(x). This includes evaluations like (f + g)(3), (f ∘ g)(2), and more. Suitable for Grades 9-11.

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