11 Components
Big Ideas
Formative Assessment Lesson
End of Unit Assessments
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Big Ideas
Formative Assessment Lesson
End of Unit Assessments
Big Idea:

### Rational functions describe the quotient of two polynomial functions.

1 week

Evidence of Understanding

• describe connections between a rational equation and the features of its graph
• describe the general shape and patterns for the graph of a rational function including domain, range, end behavior, and asymptotes
• use the equation to justify vertical asymptotes on the graph (limits on the domain)
• possible extension: use the degree of the numerator and denominator of the rational function to predict oblique asymptotes and use long division to determine their equations
• use the structure of an equation to identify ways to rewrite it and determine asymptotes (mainly via factoring but possibly also applying properties of polynomials)
• solve rational functions in the context of a situation
• build equations that model the relationship between two variables in a rational function
• connect equivalent mathematical representations (an equation to a situation, etc.) and justify the connection
• use multiple mathematical representations (equation, table, graph) to uncover solutions to a problem or answer questions for a given situation
• rewrite rational expressions in different forms using long division when necessary
• Example:  (x+4)/(x+3) = (x+3) +1/(x+3) = 1 + 1/(x+3)
• Example:  (x3 + 5x2 + 3x - 2)/(x + 1) = x2 + 6x + 9 + 7/(x + 1)
• solve rational equations and verify extraneous solutions

Develop conceptual understanding:

rational function, asymptote, extraneous solution, (+)oblique asymptote

Supporting terms to communicate:

domain, range, end behavior, degree, polynomial, roots, zeros, variable, term, binomial factor
Core Resource

A core resource supports multiple days of instruction.

• Rational Functions
This Core Resource supports students in connecting what they have learned about operations with polynomials to rational functions.
Resource:
Rational Functions

This Core Resource supports students in connecting what they have learned about operations with polynomials to rational functions.

All Resources From:
• Unit 4