Know: Understand: Do: 1 -- Essential Make sense of problems and persevere in solving them. The denominator of a rational function is critical in the graph and solution of the function. 1 -- Essential Make sense of problems and persevere in solving them. 2 -- Essential Reason abstractly and quantitatively. 3 -- Essential Construct viable arguments and critique the reasoning of others. 4 -- Essential Model with mathematics. 2 -- Essential Reason abstractly and quantitatively. 3 -- Essential Construct viable arguments and critique the reasoning of others. 4 -- Essential Model with mathematics. 5 -- Essential Use appropriate tools strategically. 5 -- Essential Use appropriate tools strategically. 6 -- Essential Attend to precision. 7 -- Essential Look for and make use of structure. 8 -- Essential Look for and express regularity in repeated reasoning. Solve equations involving rational and/or radical expressions (e.g., 10/(x + 3) + 12/(x 2) = 1 or x2 + 21x = 14). 6 -- Essential Attend to precision. 7 -- Essential Look for and make use of structure. 8 -- Essential Look for and express regularity in repeated reasoning. CC.2.2.HS.D.6 -- Essential Extend the knowledge of rational functions to rewrite in equivalent forms. Solve equations involving rational and/or radical expressions (e.g., 10/(x + 3) + 12/(x 2) = 1 or x2 + 21x = 14). Page 1 of 3
Which standards are students learning in this unit? A2.1.2.1.1 -- Essential Use exponential expressions to represent rational numbers. A2.1.2.1.2 -- Essential Simplify/evaluate expressions involving positive and negative exponents and/or roots (may contain all types of real numbers exponents should not exceed power of 10). A2.1.2.1.3 -- Essential Simplify/evaluate expressions involving multiplying with exponents (e.g., x 6 x 7 = x 13 ), powers of powers (e.g., (x 6 ) 7 = x 42 ) and powers of products (e.g., (2x 2 ) 3 = 8x 6 ). Note: Limit to rational exponents. A2.1.2.2.2 -- Essential Simplify rational algebraic expressions. Solve equations involving rational and/or radical expressions (e.g., 10/(x + 3) + 12/(x 2) = 1 or x 2 + 21x = 14). A2.2.1.1.3 -- Essential Determine the domain, range, or inverse of a relation. A2.2.2.1.1 -- Essential Create, interpret, and/or use the equation, graph, or table of a polynomial function (including quadratics). A2.2.2.1.4 -- Essential Translate from one representation of a function to another (graph, table, and equation). 1 -- Essential Make sense of problems and persevere in solving them. 2 -- Essential Reason abstractly and quantitatively. 3 -- Essential Construct viable arguments and critique the reasoning of others. 4 -- Essential Model with mathematics. 5 -- Essential Use appropriate tools strategically. 6 -- Essential Attend to precision. Page 2 of 3
7 -- Essential Look for and make use of structure. 8 -- Essential Look for and express regularity in repeated reasoning. CC.2.2.HS.D.6 -- Essential Extend the knowledge of rational functions to rewrite in equivalent forms. A2.1.2.2.2 -- Essential Simplify rational algebraic expressions. Solve equations involving rational and/or radical expressions (e.g., 10/(x + 3) + 12/(x 2) = 1 or x 2 + 21x = 14). Page 3 of 3
Key Learning: The denominator of a rational function is critical in the graph and solution of the function. Unit Essential Question(s): How do we graph a rational function whose graph is discontinuous in the coordinate plane? Concept: Concept: Concept: inverse and joint variations graph simple rational funcitons graph rational functions with higher A2.1.3.1.2, A2.2.1.1.3 CC.2.2.HS.D.6, A2.2.1.1.3 degree polynomials CC.2.2.HS.D.6, A2.1.2.2.2, A2.1.3.1.2 What are the differences between direct, inverse How do you graph simple rational functions? How do you find vertical and horizontal and joint variationj? (A) (A) asymptotes of a rational function? (A) A2.2.1.1.3 A2.2.1.1.3 A2.1.2.2.2, A2.1.3.1.2 inverse variation, constant variation, joint vertical asymptote, horizontal asymptote, rational function, point of discontinuity, vertical variation branch, rational function, domain, range asymptote, horizontal asymptote, end behavior Concept: Concept: Concept: multiply and divide rational adding and subtracting rational expressions expressions A2.1.2.1.2, A2.1.2.2.2, A2.1.2.1.1, A2.1.2.1.3 A2.1.3.1.2, A2.1.2.1.2, A2.1.2.2.2 solving rational equations A2.1.3.1.2 How do you multiply, divide rational How do you add or subtract rational expressions What are the steps for solving rational expressions? (A) with different denominators? How do you simplify a complex fraction? (A) equations? (A) A2.1.2.1.2, A2.1.2.2.2, A2.1.2.1.1, A2.1.2.1.3 A2.1.3.1.2 A2.1.2.1.2, A2.1.2.2.2 simplest form, reciprocal complex fraction cross multiplying, extraneous solution Page 1 of 2
Concept: Concept: Concept: function characteristics CC.2.2.HS.D.6, A2.2.2.1.1, A2.2.2.1.4 How do you compare functions represented in different ways? (A) A2.2.2.1.1, A2.2.2.1.4 increasing, decreasing, odd function, even function Additional Information: graph paper, graphing calculator, textbook Attached Document(s): Page 2 of 2
Vocab Report for Concept: inverse and joint variations inverse variation - constant variation - joint variation - Concept: graph simple rational funcitons vertical asymptote - horizontal asymptote - branch - rational function - domain - range - Concept: graph rational functions with higher degree polynomials rational function - point of discontinuity - vertical asymptote - horizontal asymptote - end behavior - Concept: multiply and divide rational expressions simplest form - reciprocal - Concept: adding and subtracting rational expressions complex fraction - Concept: solving rational equations cross multiplying - extraneous solution - Concept: function characteristics increasing - decreasing - odd function - even function - Page 1 of 1