Day 5 examples u5w14

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Day 5 examples u5w14

  1. 1. Characteristics of Polynomial Functions Recall, standard form of a polynomial: + ... + a x is a variable the coefficients a are real numbers of a polynomial is the highest power of the variable in the equation. leading coefficient is the coefficient of the
  2. 2. The graph of a polynomial is smooth and continuous - no sharp corners and can be drawn without lifting a pencil off a piece of paper Polynomials can be described by their degree: - Odd-degree polynomials (1, 3, 5, etc.) - Even-degree polynomials (2, 4, etc.) - Linear (degree 1) - Quadratic (degree 2) (degree 3) - Quartic (degree 4) - Quintic (degree 5)
  3. 3. Positive, odd falls to the left at - rises to the right at +∞ End behaviour: Negative, odd rises to the left at - falls to the right at +∞
  4. 4. Positive, even rises to the left at - rises to the right at +∞ End behaviour: Negative, even falls 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 to decreasing is called a local maximum point A point where the graph changes from decreasing to creasing is called a local minimum point A graph of a polynomial function of degree n can have at most n x-intercepts and at most (n - 1) local maximum or minimum points
  7. 7. Polynomial Matching What to look for? - degree - leading coefficient - even or odd - number of x-intercepts - number of local max/min - end behaviour
  8. 8. Graphing Polynomials of any polynomial fuction y = f(x) correspond to the x-intercepts of the graph and the roots of the equation, f(x) = 0. ex. f(x) = (x - 1)(x - 1)(x + 2) If a polynomial has a factor that is repeated then x = a is a zero of multiplicity x = 1 (zero of even multiplicity) x = -2 (zero of odd multiplicity) sign of graph changes sign of graph does not change
  9. 9. ex. f(x) = (x - 1)2(x + 3)2
  10. 10. ex. g(x) = -(x + 2)3(x - 1)2

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