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Week 2 Linear Functions Presentation

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Week 2 4.1 Linear Functions The Train (Example We will use for all forms) Suppose a train travels a long distance, and maintains a constant speed of 83 meters per second for a period of time once it is 250 meters from the station. Representing Linear Functions Word form: What is the train or function doing? The train’s distance from the station is a function of the time during which the train moves at a constant speed plus its original distance from the station when it began moving at constant speed. Function Notation: The equation of the problem with y as f(x) Equation form 𝑦=𝑚𝑥+𝑏 Function notation: 𝑓(𝑥)=𝑚𝑥+𝑏 D(t) = 83t + 250 Distance is a function of time Representing Linear Functions (cont.) Tabular Form: Showing the function as a table Graphical Form: Plotting the function’s equation on a graph Linear Functions A function whose graph is a line, in other words no variables will be raised to an exponent f(x) = mx + b M = slope, or rate of change B = starting point, y-intercept is (0,b) Increasing, Decreasing, Constant Increasing = positive slope or m value Decreasing = negative slope or m-value Constant = slope equals 0, f(x) = y Example 2: The average teen sends 60 texts/day. Determine whether the following scenarios are increasing, decreasing or constant. The total number of texts a teen sends is considered a function of time in days. The input is the number of days, and output is the total number of texts sent. f(x) = ...
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