Unit 11: Rational Functions

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Essential Questions: 
  • When we find the variable in the denominator, what are the fundamental differences with other functions that we should be aware of?
  • How are rational functions related to the parent function of 1/x?
  • Why are there restrictions placed on rational functions?
  • What does end behavior mean?
Content: 
  • Definition of rational function: r(x) = p(x)/q(x), where p and q are polynomials.
  • Review operations on rational expressions (addition, subtraction, multiplication, and division).
  • Simplifying complex fractions.
  • Recognize and find the domain, range, and zeroes of a rational function.
  • Recognize the difference between the vertical and horizontal (if present) asymptotes, and be able to find them.
  • Long division of polynomials.
  • Find the slant asymptote of a rational function when it has one.
Skills and Processes: 
  • Simplifying rational expressions.
  • Graphing Rational Functions (domain, range, asymptotes, zeroes, end behavior).
  • Long division of polynomials
  • Transformations on 1/x