Key Learning:
Rational functions are a ratio of polynomials. Performing operations
with rational expressions follows the same general procedures as with
rational numbers. The graphs of rational functions have asymptotes
wherever the domain is undefined.
Unit Essential Question:
How are rational functions and polynomials related?
How are the graphs of rational functions different from the graphs of polynomials?
Concept 1:
Simplifying Rational Expressions |
Concept 2:
Operations with Rational Expressions |
Concept 3:
Solving Rational Equations
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Lesson Essential Questions:
How are properties of exponents used in simplifying rational expressions?
How is factoring used in simplifying rational expressions?
(Optional Enrichment) How are properties of exponents used in solving problems involving scientific notation?
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Lesson Essential Questions:
How do you multiply and divide rational expressions?
How do you add and subtract rational expressions?
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Lesson Essential Questions:
How do you solve rational equations?
Why do rational equations sometimes have extraneous solutions?
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Vocabulary:
rational expression, properties of exponents, greatest common factor, sum (or difference) of cubes, quadratic form, factor by grouping
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Vocabulary:
reciprocal, least common multiple, least common denominator
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Vocabulary:
rational equation, proportion, extraneous solution
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Concept 4:
Graphing Rational Functions |
Concept 5: (Optional)
Modeling with Rational Functions
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Lesson Essential Questions:
How do you use transformations to sketch the graph of a rational function?
How are the domain and range of a rational function different from the other functions we have studied?
How do you write the equation of a rational function given its graph or characteristics?
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Lesson Essential Questions:
How do you decide when variables in an equation vary directly, inversely, or jointly?
How do you determine the constant of variation when variables in an equation vary directly, inversely, or jointly?
How do you model real world problems using rational functions?
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Vocabulary:
parent graph, hyperbola, restricted domain, vertical asymptote, horizontal asymptote, hole
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Vocabulary:
direct variation, inverse variation, joint variation, constant of variation
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