\( f(x)=\left\{\begin{array}{ll}x+2 & \text { if } x<2 \\ x+1 & \text { if } x \geq 2\end{array}\right. \)

Did you know that piecewise functions like the one you've shared are often used to model real-life situations? For instance, they can represent scenarios where different rules apply under varying conditions, such as tax rates based on income brackets or shipping costs that change depending on the weight of a package. This helps us better analyze situations where a single linear equation just won't cut it! When working with piecewise functions, one common mistake is forgetting to clearly define the points where the function changes. In this case, at \( x = 2 \), it's crucial to note that the function shifts from \( x + 2 \) to \( x + 1 \). Be careful with evaluating limits or determining continuity at such boundary points, as it can lead to confusion if not handled correctly!