To find the value of \( f(2) \), you need to know the function \( f(x) \). The function \( f(x) \) can be provided in different forms, such as a set of ordered pairs, a table, or a formula.

Here’s how you can find \( f(2) \) depending on the form of \( f(x) \):

### 1. **If \( f(x) \) is Given as Ordered Pairs:**
Suppose the function \( f(x) \) is given as a set of ordered pairs like this:
\[
f(x) = \{(x_1, y_1), (x_2, y_2), (x_3, y_3), \ldots\}
\]
To find \( f(2) \), look for the pair where the first element (the input) is 2. The second element of this pair will be the value of \( f(2) \).

**Example:** If \( f(x) = \{(1, 3), (2, 5), (3, 7)\} \), then \( f(2) = 5 \).

### 2. **If \( f(x) \) is Given as a Formula:**
If the function \( f(x) \) is defined by a formula, like \( f(x) = 2x + 3 \), you would substitute \( x = 2 \) into the formula to find \( f(2) \).

**Example:** If \( f(x) = 2x + 3 \), then:
\[
f(2) = 2(2) + 3 = 4 + 3 = 7
\]

### 3. **If \( f(x) \) is Given in a Table:**
If \( f(x) \) is given in a table, find the row where the \( x \)-value is 2, and the corresponding \( y \)-value in that row will be \( f(2) \).

**Example:**

\[
\begin{array}{c|c}
x & f(x) \\
\hline
1 & 4 \\
2 & 6 \\
3 & 8 \\
\end{array}
\]
Here, \( f(2) = 6 \).

### 4. **If \( f(x) \) is Defined Piecewise:**
If the function is piecewise, check which part of the function applies to \( x = 2 \) and then substitute 2 into that part of the function.

**Example:**
\[
f(x) = \begin{cases} 
x^2 & \text{if } x < 3 \\
x + 1 & \text{if } x \geq 3 
\end{cases}
\]
Since \( 2 < 3 \), use \( f(x) = x^2 \):
\[
f(2) = 2^2 = 4
\]

If you provide the function \( f(x) \), I can give you the exact value of \( f(2) \).

Would you like more details or have any further questions? Here are some related questions to consider:

1. How do you interpret ordered pairs in a function?
2. What is the general form of a linear function?
3. How do you solve for \( f(x) \) when the function is quadratic?
4. What is a piecewise function, and how is it applied?
5. How do you determine which part of a piecewise function to use?
6. How does the concept of a function apply in real-world scenarios?
7. What steps would you take to graph a function like \( f(x) \)?
8. How do you evaluate a composite function such as \( f(g(x)) \)?

**Tip:** Always substitute the value of \( x \) directly into the function and carefully simplify to find \( f(x) \).

Learn how to find the value of f(2) using ordered pairs, function formulas, and tables. Understand piecewise functions and solve examples to master function evaluation. Suitable for students in Grades 7-9.

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