For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change. 8.F.2 - Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.1 8.F.1 - Understand that a function is a rule that assigns to each input exactly one output.Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.★ A-REI.11 - Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x) find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations.Represent and solve equations and inequalities graphically A-REI.3 - Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

Solve equations and inequalities in one variable. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.

A-CED.3 - Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.

A-CED.2 - Create equations in two or more variables to represent relationships between quantities graph equations on coordinate axes with labels and scales.For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.Ĭreate equations that describe numbers or relationships. F-IF.9 - Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).F-IF.7b - Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.F-IF.7 - Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.★.Estimate the rate of change from a graph.★Īnalyze functions using different representations. F-IF.6 - Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval.For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.★ F-IF.5 - Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.Key features include: intercepts intervals where the function is increasing, decreasing, positive, or negative relative maximums and minimums symmetries end behavior and periodicity.★ F-IF.4 - For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.Interpret functions that arise in applications in terms of the context.

Domain and range of piecewise functions