Students know that a function allows us to make predictions about the distance an object moves in any time interval. Students calculate average speed of a moving object over specific time intervals.
Students know that constant rate cannot be assumed for every situation and use proportions to analyze the reasoning involved.
Students know that a function assigns to each input exactly one output.
Students know that some functions can be expressed by a formula or rule, and when an input is used with the formula, the outcome is the output.
Students relate constant speed and proportional relationships to linear functions using information from a table.
Students know that distance traveled is a function of the time spent traveling and that the total cost of an item is a function of how many items are purchased.
Students examine and recognize real-world functions, such as the cost of a book, as discrete rates.
Students examine and recognize real-world functions, such as the temperature of a pot of cooling soup, as continuous rates.
Students know that the definition of a graph of a function is the set of ordered pairs consisting of an input and the corresponding output.
Students understand why the graph of a function is identical to the graph of a certain equation.
Students use rate of change to determine if a function is a linear function.
Students interpret the equation y = mx + b as defining a linear function, whose graph is a line.
Students compare the properties of two functions represented in different ways (e.g., tables, graphs, equations and written descriptions)
Students use rate of change to compare functions (e.g., determining which function has a greater rate of change).
Students examine the average rate of change for non-linear functions and learn that, unlike linear functions, non-linear functions do not have a constant rate of change.
Students determine whether an equation is linear or non-linear by examining the rate of change.