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:

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)$$.