in standard form. Students will solve applications of polynomials. Domain: Interpreting Functions Enduring Understanding(s) 3.5 Graphing Rational Functions (Coburn) Vocabulary Cluster: Analyze functions using different 3.5 Rational Functions and Their Graphs Rational function, reciprocal square function, Real situations can be modeled and representations. (Blitzer) asymptotic behavior, vertical asymptote, solved by using various functions. horizontal asymptote, arrow notation, Graphs of functions can explain the Graph rational functions, identifying zeros, observed local and global behavior of a asymptotes (including slant), and holes when Task(s) function. suitable factorizations are available, and Writing in Math Asymptotes and Rational Functions showing end-behavior. Why is a function called “rational?” What Essential Question(s) could make a function “irrational?” How do What are the similarities and differences these mathematical terms differ from common between linear, quadratic, and polynomial English usage of the same terms? Select tasks from the following (pp.12-157): functions? Objective(s): Students will identify horizontal and Additional Resource(s) vertical asymptotes. Students will find the domains of a rational function. Students will apply the concept of “multiplicity” to rational graphs. Students will find the horizontal asymptotes of a rational function. Students will graph general rational functions. Students will solve applications of rational functions. Domain: N-NE – Number Expressions Enduring Understanding(s) 3.6 Additional Insights Into Rational Vocabulary Functions (Coburn) Cluster: Represent, intercept, compare, and Oblique asymptote Real world situations can be modeled and simplify number expressions. P.6 Rational Expressions (Blitzer) solved by using various functions. Graphs of functions can explain the N-NE.A.5 Understand that rational expressions
in standard form. Students will solve applications of polynomials. Domain: Interpreting Functions Cluster: Analyze functions using different representations. Graph rational functions, identifying zeros, asymptotes (including slant), and holes when suitable factorizations are available, and showing end-behavior. Enduring Understanding(s) Real situations can be modeled and solved by using various functions. Graphs of functions can explain the observed local and global behavior of a function. Essential Question(s) What are the similarities and differences between linear, quadratic, and polynomial functions? Objective(s): Students will identify horizontal and vertical asymptotes. Students will find the domains of a rational function. Students will apply the concept of “multiplicity” to rational graphs. Students will find the horizontal asymptotes of a rational function. Students will graph general rational functions. Students will solve applications of rational functions. 3.5 Graphing Rational Functions (Coburn) 3.5 Rational Functions and Their Graphs (Blitzer) Task(s) Asymptotes and Rational Functions Select tasks from the following (pp.12-157): Additional Resource(s) Vocabulary Rational function, reciprocal square function, asymptotic behavior, vertical asymptote, horizontal asymptote, arrow notation, Writing in Math Why is a function called “rational?” What could make a function “irrational?” How do these mathematical terms differ from common English usage of the same terms? Domain: N-NE – Number Expressions Cluster: Represent, intercept, compare, and simplify number expressions. N-NE.A.5 Understand that rational expressions Enduring Understanding(s) Real world situations can be modeled and solved by using various functions. Graphs of functions can explain the 3.6 Additional Insights Into Rational Functions (Coburn) P.6 Rational Expressions (Blitzer) Vocabulary Oblique asymptote
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