Did you know that piecewise functions, like the one you’ve shared, are often used to describe real-world phenomena where different rules apply in various situations? For instance, they can model scenarios like tax brackets where income tax rates change based on income thresholds, or physical situations where different forces or motions come into play depending on conditions, such as speed limits that differ for different types of vehicles!

When working with piecewise functions, one common mistake is forgetting to check the continuity at the point where the definition changes—in your case, at . Make sure that the value of the function from both sides match at that point! Here, since from both and , your function is indeed continuous at . Keep an eye on those switch points!