Quantitative Reasoning with Functions

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Students will understand characteristics of functions
Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range.(MGSE9-12.F.IF.1)
Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. 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(MGSE9-12.F.IF.5)
Graph functions using sets of ordered pairs consisting of an input and the corresponding output(MGSE8.F.1, 2)
Students will compare and graph functions.
Calculate rates of change of functions, comparing when rates increase, decrease, or stay constant. 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(MGSE6.RP.2;MGSE7.RP.1,2,3;MGSE8.F.2,5; MGSE9-12.F.IF.6)
Graph by hand simple functions expressed symbolically (use all four quadrants)(MGSE9- 12.F.IF.7)
Interpret the equation y = mx + b as defining a linear function whose graph is a straight line(MGSE8.F.3)
Use technology to graph non-linear functions(MGSE8.F.3, MGSE9-12.F.IF.7)
Analyze graphs of functions for key features (intercepts, intervals of increase/decrease, maximums/minimums, symmetries, and end behavior) based on context(MGSE9-12.F.IF.4,7)
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions)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 great rate of change(MGSE8.F.2)
Students will construct and interpret functions
Write a function that describes a relationship between two quantities(MGSE8.F.4, MGSE9- 12.F.BF.1)
Use variables to represent two quantities in a real world problem that change in relationship to one another (conceptual understanding of a variable)(MGSE6.EE.9)

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