8.FGR.5

Describe the properties of functions to define, evaluate, and compare relationships, and use functions and graphs of functions to model and explain real phenomena.

8.FGR.5.1Show and explain that a function is a rule that assigns to each input exactly one output.8.FGR.5.2Within realistic situations, identify and describe examples of functions that are linear or nonlinear. Sketch a graph that exhibits the qualitative features of a function that has been described verbally.8.FGR.5.3Relate the domain of a linear function to its graph and where applicable to the quantitative relationship it describes.8.FGR.5.4Compare properties (rate of change and initial value) of two functions used to model an authentic situation each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).8.FGR.5.5Write and explain the equations y = mx + b (slope-intercept form), Ax + By = C (standard form), and (y – y_1) = m(x-x_1) (point-slope form) as defining a linear function whose graph is a straight line to reveal and explain different properties of the function.8.FGR.5.6Write a linear function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.8.FGR.5.7Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x,y) values, including reading these from a table or from a graph.8.FGR.5.8Explain the meaning of the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.8.FGR.5.9Graph and analyze linear functions expressed in various algebraic forms and show key characteristics of the graph to describe applicable situations.
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