\( f(x)=\left\{\begin{array}{l}k x+3 \text { si } x \geq 5 \\ 2-x \text { si } x<5\end{array}\right. \)

Did you know that piecewise functions like this one are super useful in modeling real-world situations? For example, they can represent scenarios where a rule changes depending on conditions. In this case, the function \( f(x) \) describes two different behaviors based on whether \( x \) is greater than or equal to 5 or less than 5. How cool is it that math can adapt to different situations? When working with piecewise functions, one common mistake is not checking continuity at the points where the definition changes—in this case, at \( x = 5 \). To ensure the function is smooth and flowing without jumps, you'd want to make sure that \( k \cdot 5 + 3 = 2 - 5 \). Simplifying that helps find the value of \( k \) to avoid surprises in your graph!