And that's why you should choose which function goes with which interval. If ##x \in [0. 3]## you use the formula y = -x + 3. If ##x \in (3, 5)##, you use the formula y = 2x - 6.Rijad Hadzic said:
Mark44 said:
Yes. At x = 3, both functions have y-values of 0, so it doesn't matter how you define the endpoints of the two intervals.Rijad Hadzic said:
A piecewise function is a function that is defined by different expressions for different intervals, or "pieces", of the input. This means that the function may have different rules for different parts of the input domain. In contrast, a regular function has one single rule that applies to the entire input domain.
To find the expression for a piecewise function, you will need to carefully examine the graph and identify the different intervals and their corresponding rules. Then, you can write out the expression for each interval separately, making sure to incorporate any necessary adjustments, such as shifting or reflecting the graph.
Yes, a piecewise function can have as many pieces as needed to accurately represent the different rules for different parts of the input domain. This means that a piecewise function can have two, three, four, or even more pieces, depending on the complexity of the function.
Piecewise functions are commonly used in fields such as economics, engineering, and physics to model real-life situations that involve changing rules or conditions. For example, a piecewise function could be used to model a company's production costs, where different rules apply for different levels of production.
Yes, some common mistakes when working with piecewise functions include forgetting to include all necessary intervals and their corresponding rules, not considering any necessary adjustments to the graph, and not carefully labeling the intervals and their corresponding rules. It is important to be thorough and precise when working with piecewise functions to accurately represent the function's behavior.
