New day 5 examples

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New day 5 examples

  1. 1. Characteristics of Polynomial FunctionsRecall, standard form of a polynomial:+ ... + ax is a variablethe coefficients a are real numbersof a polynomial is the highest power ofthe variable in the equation.leading coeffcient is the coeffcient of the- Linear (degree 1)- Quadratic (degree 2)(degree 3)- Quartic (degree 4)- Quintic (degree 5)
  2. 2. The graph of a polynomial is smooth and continuous- no sharp corners and can be drawn without lifting apencil off a piece of paperPolynomials can be described by their degree:- Odd-degree polynomials (1, 3, 5, etc.)- Even-degree polynomials (2, 4, etc.)
  3. 3. Positive, oddfalls to the left at -rises to the right at +∞End behaviour:Negative, oddrises to the left at -falls to the right at +∞
  4. 4. Positive, evenrises to the left at -rises to the right at +∞End behaviour:Negative, evenfalls to the left at -falls to the right at +∞
  5. 5. Can also have a degree of 0..Constant function
  6. 6. A point where the graph changes from increasing todecreasing is called a local maximum pointA point where the graph changes from decreasing tocreasing is called a local minimum pointA graph of a polynomial function of degree n can have atmost n x-intercepts and at most (n - 1) local maximum orminimum points
  7. 7. Polynomial MatchingWhat to look for?- degree- leading coefficient- even or odd- number of x-intercepts- number of local max/min- end behaviour
  8. 8. Graphing Polynomialsof any polynomial fuction y = f(x)correspond to the x-intercepts of the graph and theroots of the equation, f(x) = 0.ex. f(x) = (x - 1)(x - 1)(x + 2)If a polynomial has a factor that is repeatedthen x = a is a zero of multiplicityx = 1 (zero of even multiplicity)x = -2 (zero of odd multiplicity)sign of graph changessign of graph does not change

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