A function is defined as an assignment to each input, exactly one output. Students learn that the assignment of some functions can be described by a mathematical rule or formula. Students consider functions of discrete and continuous rates and understand the difference between the two.
Students apply their knowledge of linear equations and their graphs to graphs of linear functions. Students relate a function to an input/output machine: a number or piece of data, known as the input, goes into the machine, and a number or piece of data, known as the output, comes out of the machine. Students inspect the rate of change of linear functions and conclude that the rate of change is the slope of the graph of a line. They learn to interpret the equation 𝑦 = 𝑚𝑥 + 𝑏 as defining a linear function whose graph is a line.
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