Chapter 3 Section 2

Notes

Linguistic Mapping Exercises

Knowledge Checks

  1. Determine whether the following rational function in simplest form: \[f(x)=\frac{x(x-3)^2}{x^2(x+3)}.\]
  2. Find the zeros and poles of the given function and list the order or multiplicity as well: \[f(x)=\frac{(x+2)^2(x-2)}{x^3(x+4)}.\]
  3. For the following function, list the poles of the function and the order of each pole, the vertical asymptotes of \(f\), the horizontal asymptote of \(f\), sketch the denominator of \(f\) and then use inversion to sketch the function: \[f(x)=\frac{1}{20(x+11)^5(x+6)^3(x-1)^2(x-3)^4(2x-7)^5}.\]
  4. List and classify all asymptotes of \[f(x)=\frac{x^2-4}{(x+9)^2(x-6)}.\]

Remember, do the knowledge checks before checking the solutions. ## Practice Problems

Practice Problems

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