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Lesson plan

See how the structure of a rational function can reveal features of the graph by exploring equivalent 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 graph by exploring equivalent rational expressions

Big Ideas: The properties of fractions extend to rational expressions and algebraic fractions. The structure of an expression can reveal properties of the function it defines. The structure of a rational function can reveal its horizontal asymptote. In this task, students explore the equivalence of two rational expressions: (a+bx)/x and a/x+b. 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 horizontal asymptote--with the function, and to notice that structure can reveal properties of the function. Specifically, students observe that writing the function f(x)=(a+bx)/x in its equivalent form f(x)=a/x+b may be helpful in revealing the location of the horizontal asymptote. Vocabulary: expressions, equivalent, rational, function, simplify, asymptote, graph Special Materials: Graph paper