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Lesson plan

See how the structure of a rational function can reveal features of the function and its graph by simplifying rational expressions

teaches Common Core State Standards HSA-APR.D.6 http://corestandards.org/Math/Content/HSA/APR/D/6

See how the structure of a rational function can reveal features of the function and its graph by simplifying rational expressions

Big Ideas: The structure of an expression can reveal properties of the function it defines, and the structure of a rational function can reveal its asymptotes. A rational function may have an oblique asymptote, where its value approaches a line with a non-zero slope as the independent variable gets larger. In this task, students explore the importance of equivalent rational expressions in the form f(x)=(ax^2+bx+c)/x. Expressions of this type are used to define functions, which are then graphed. Students are encouraged to connect features of the graph--and in particular the location of the oblique asymptote--with the function, and to notice that structure can reveal properties of the function. Specifically, students observe that writing the function f(x)=(ax^2+bx+c)/x in its equivalent form f(x)=c/x+ax+b may be helpful in revealing the location of the oblique asymptote. Vocabulary: expressions, equivalent, rational, function, simplify, asymptote, graph, oblique Special Materials: Graph paper