Reading schedules

Learning Objectives Model a real-world schedule as a mathematical function. Identify the independent and dependent variables, domain, and range from a given schedule. Represent a schedule as a piecewise-defined function. Evaluate a schedule function for a specific input time to determine an output (e.g., location, activity). Calculate the average rate of change between two points in a schedule and interpret its meaning (e.g., average speed). Analyze discontinuities in a schedule function, representing events like instantaneous changes in activity. Ever wondered how your GPS calculates your arrival time or how a project manager knows if they're on track? 🗺️ It all comes down to treating schedules as mathematical functions! In this tutorial, we will explore how to interp...

TermDefinitionExample Schedule as a FunctionA relationship where each specific point in time (the input) corresponds to exactly one state, such as a location, task, or status (the output).If L(t) represents the location of a train at time 't', then L(10:30 AM) = 'Central Station'. The input is 10:30 AM, and the output is 'Central Station'. Independent VariableThe input of the function, which can be chosen freely within the domain. In schedules, this is almost always time.For a school day schedule, the time of day (e.g., 9:15 AM) is the independent variable. Dependent VariableThe output of the function, whose value depends on the input. In schedules, this is the event, location, or status.For a school day schedule, the subject being taught (e.g., 'Complex...

Function Notation for Schedules y = f(x) \rightarrow \text{State} = S(t) We use function notation to formally express the relationship in a schedule. 'S(t)' denotes the state (e.g., location, task) at a specific time 't'. Evaluating S(t) means finding the state at that exact time. Average Rate of Change \text{Average Rate of Change} = \frac{\Delta y}{\Delta x} = \frac{f(x_2) - f(x_1)}{x_2 - x_1} For schedules, this formula calculates how the dependent variable changes with respect to time. For a schedule of a moving object, this calculates its average velocity between two points in time. Let D(t) be the distance from a starting point. The average velocity from time t1 to t2 is (D(t2) - D(t1)) / (t2 - t1). Piecewise Function Definition f(x) = \begin{...