Summary
Highlights
A piecewise function is defined by two or more equations, each applying to a specific interval of the domain. The video introduces how to find values and graph these functions.
Given a function with two conditions (3x + 2 for x >= 0, and -x^2 + 3 for x < 0), the video demonstrates how to evaluate f(0) and f(-3) by selecting the appropriate equation based on the input value's condition.
Another example is provided with conditions (x + 3 for x >= 0, and -x^2 + 3 for x < 0). The process for finding f(-5) and f(3) is shown, emphasizing the importance of choosing the correct function based on the input.
The video introduces Desmos as a tool for graphing piecewise functions. It demonstrates how to input the function and its conditions to visualize the graph, highlighting how restrictions affect the plot.
A real-world example of a mobile plan is presented: 300 pesos for 100 free text messages, with 1 peso per message for anything over 100. The video explains how to represent this scenario using a piecewise function, with T(M) as cost as a function of messages M.
Another practical application involves tricycle fares: 20 pesos for the first 1 kilometer, plus 5 pesos for every additional half-kilometer. The video details how to formulate this into a piecewise function, F(D), where D is the distance in kilometers, and demonstrates how to calculate fares for different distances.