Chapter 3 Section 1

Notes

Linguistic Mapping Exercises

Knowledge Checks

  1. Take \(f\) to be the function that is given by \[f(x) = 6(x-2)^2 - 15.\]
    1. Determine the axis of symmetry and vertex of \(f\).
    2. Find all roots (\(x\)-intercepts) of \(f\).
    3. Sketch \(f\).
    4. Solve \(f>0\).
  2. Find and classify the extremal points of \(f\), where \[f(x) = -10 x^2 + 10 x + \tfrac{1}{2}.\]
  3. Find polynomials \(q\) and \(r\) so that \(\frac{r(x)}{x - 4}\) is a proper fraction and \[5x^3+10x^2-5 = q(x)(x - 4) + r(x).\]
  4. Write \(4 x^3 - 32 x^2 - 212 x + 240\) as a product of linear factors given that \(x=-5\) is a root or zero.
  5. Take \(f\) to be the polynomial function that is given by \[f(x) = 20(x+11)^5(x+6)^3(x-1)^2(x-3)^4(2x-7)^5.\] List the zeros of \(f\) together with their orders.
  6. Determine the leading term of the polynomial \(f\) that is given by \[f(x) = 20(x+11)^5(x+6)^3(x-1)^2(x-3)^4(2x-7)^5.\] Describe the asymptotic behavior of \(f\).
  7. Sketch the polynomial \(f\), where \[f(x) = 20(x+11)^5(x+6)^3(x-1)^2(x-3)^4(2x-7)^5.\]

Remember, do the knowledge checks before checking the solutions.

Practice Problems

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