Students will extend their understanding of inverse functions to functions with a degree higher than 1, and factor and simplify rational expressions to reveal domain restrictions and asymptotes.
In Unit 4, Rational and Radical Functions, students will extend their understanding of inverse functions to functions with a degree higher than 1. Alongside this concept, students will factor and simplify rational expressions and functions to reveal domain restrictions and asymptotes. Students will become fluent in operating with rational and radical expressions and use the structure to model contextual situations. In this unit, students will also revisit the concept of an extraneous solution, first introduced in Unit 1, through the solution of radical and rational equations.
The unit begins with Topic A, where there is a focus on understanding the graphical and algebraic connections between rational and radical expressions, as well as fluently writing these expressions in different forms. In Topic B, students delve deeper into rational equations and functions and identify characteristics such as the $$x$$- and $$y$$-intercepts, asymptotes, and removable discontinuities based on the relationship between the degree of the numerator and denominator of the rational expression. Students will also connect these features with the transformation of the parent function of a rational function. In Topic C, students solve rational and radical equations, identifying extraneous solutions, then modeling and solving equations in situations where rational and radical functions are necessary. Students will connect the domain algebraically with the context and interpret solutions.
Pacing: 20 instructional days (18 lessons, 1 flex day, 1 assessment day)
This assessment accompanies Unit 4 and should be given on the suggested assessment day or after completing the unit.
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Internalization of Standards via the Unit Assessment
Internalization of Trajectory of Unit
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Vertical and horizontal asymptote | Invertible functions |
Rational function | Zero product property |
Rational expression | Asymptotic discontinuities (infinite) |
Domain restriction | Removable discontinuities |
Square root / cube root | End behavior |
Extraneous solutions | Sign chart |
Key: Major Cluster Supporting Cluster Additional Cluster
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