ok i dont get it , so , for solving ... for example a) : you look at the graph and lookthe value where in the g function is 3 and then why is 2???

Let's break down how to evaluate \((f \circ g)(3)\) step by step using the graph.

### Expression: \((f \circ g)(3)\)

This expression means you're looking for \(f(g(3))\). Here’s how you do it:

1. **Step 1: Find \(g(3)\)**
   - Go to the graph of \(g(x)\) and locate the point where \(x = 3\). 
   - Look at the corresponding \(y\)-value at this \(x\) position on the \(g(x)\) graph.
   - From the graph, \(g(3)\) corresponds to the \(y\)-value of \(2\). So, \(g(3) = 2\).

2. **Step 2: Use the result \(g(3) = 2\) to find \(f(g(3))\)**
   - Now, substitute \(g(3) = 2\) into the function \(f(x)\). So, you now need to find \(f(2)\).
   - Go to the graph of \(f(x)\) and find the point where \(x = 2\).
   - Look at the corresponding \(y\)-value at this \(x\) position on the \(f(x)\) graph.
   - From the graph, \(f(2)\) corresponds to the \(y\)-value of \(0\). So, \(f(2) = 0\).

So, \((f \circ g)(3) = f(g(3)) = f(2) = 0\).

### Why is \(g(3) = 2\)?
- On the graph of \(g(x)\), when \(x = 3\), you look at the height of the graph (the \(y\)-value) at this \(x\) position. The height at \(x = 3\) is 2, so \(g(3) = 2\).

### Visual Explanation:
- Imagine the graph as a landscape. The \(x\)-axis tells you where you are horizontally, and the \(y\)-axis tells you how high you are vertically.
- When you're "standing" at \(x = 3\) on the graph of \(g(x)\), you "see" that you're at a height of 2, meaning \(g(3) = 2\).

Does this explanation help clarify the process? Would you like to go through another example in more detail?

Explore how to evaluate function composition using graphical representation. Learn with detailed steps and examples on how to find (f ∘ g)(3) from given functions and graphs. Suitable for high school students studying functions and graph theory.

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