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Polynomial Functions. Rational Functions. Solving Inequalities. Finding Roots. 100. 100. 100. 100. 200. 200. 200. 200. 300. 300. 300. 300. 400. 400. 400. 400. 500. 500. 500. 500. Polynomial Functions 100. Use the graph of f ( x ) to find the following: Domain

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  1. Polynomial Functions Rational Functions Solving Inequalities Finding Roots 100 100 100 100 200 200 200 200 300 300 300 300 400 400 400 400 500 500 500 500

  2. Polynomial Functions 100 Use the graph of f(x) to find the following: • Domain • Roots • Equation

  3. A: Polynomial Functions 100 Domain: All Real Numbers Roots: x = -3, 2 Equation:

  4. Polynomial Functions 200 • Lowest possible degree • End behavior • # of turning points • Roots and their multiplicity)

  5. A: Polynomial Functions 200 • Degree 3 or greater (must be odd) • 2 Turning Points • Root x = -2 multiplicity 1 Root x = 1 multiplicity 2

  6. Polynomial Functions 300 • Does the graph have any symmetry? • Is it even, odd, or neither? • What ‘family’ does it belong to?

  7. A: Polynomial Functions 300 • Symmetric with respect to origin • Odd function • Cubic family

  8. Polynomial Functions 400 Find the equation of lowest degree possible from the given graph of f(x).

  9. A: Polynomial Functions 400

  10. Polynomial Functions 500 Find the equation of lowest degree possible from the graph of f(x) given the y-intercept is

  11. A: Polynomial Functions 500

  12. Rational Functions 100 Describe how the graph of f(x) differs from the graph of g(x).

  13. A: Rational Functions 100 The graph of f(x) is the graph of g(x) with the following changes: • reflected across the x –axis • Moved right three units • Moved up two units

  14. Rational Functions 200 Use the function to find the following: • Hole(s) (x-value) • Asymptote(s) • Intercept(s) • Domain

  15. A: Rational Functions 200 • Hole(s) (x-value): none • Asymptote(s) VA: x = 3 HA: y = -3 • Intercept(s): (0, 0) • Domain: {x | x ≠ 3}

  16. Rational Functions 300 Use the graph of f(x) to find the following: • Hole(s) (x-value) • Asymptote(s) • Intercept(s) • Domain

  17. A: Rational Functions 300 • Hole(s) (x-value) x = 2 • Asymptote(s) HA: y = -2 VA: x = -2 • Intercept(s) (0, 3) and (3, 0) • Domain {x | x ≠ ±2}

  18. Rational Functions 400 Us the graph of f(x) to find all pertinent information including the equation. Note the points (0, 0) and (1, 0) are on the graph.

  19. A: Rational Functions 400 Hole: (-6, 7) VA: x = -4, 3 HA: y = 3 Int: (0, 0) and (1, 0) Domain: {x | x ≠ -6, -4, 3}

  20. Rational Functions 500 Use the given function to find all pertinent information and graph.

  21. A: Rational Functions 500 Hole: (-2, 3.5) VA: x = 0 OA: y = x2 Int: (-1, 0) Domain: {x | x ≠ -2, 0}

  22. Solving Inequalities 100 Use the graph to determine when f(x) < 0. Give your answer in interval notation.

  23. A: Solving Inequalities 100 (-2, 1) U (1, ∞) f(x) < 0 -2 1 neg pos. neg

  24. Solving Inequalities 200 Use the graph to determine when f(x) ≥ 0. Give your answer in interval notation.

  25. A: Solving Inequalities 200 (-∞, -3] U (-2, 2) U [3, ∞) f(x) ≥ 0 -3 -2 3 3 neg pos. pos. neg pos.

  26. Solving Inequalities 300 Solve for x: give you answer in interval notation.

  27. A: Solving Inequalities 300 -4 2 pos neg pos (-4, 2) U (2, ∞)

  28. Solving Inequalities 400 Solve for x: give you answer in interval notation.

  29. A: Solving Inequalities 400 -3 0 3 pos. neg neg pos. (-3, 0) U (0, 3)

  30. Solving Inequalities 500 Solve for x: give you answer in interval notation.

  31. A: Solving Inequalities 500 [-7, -1) U (3, ∞) -7 -1 3 neg pos neg pos.

  32. Finding Roots 100 Find all the roots of the following function.

  33. A: Finding Roots 100 x = -5, -4, 1 Look for:

  34. Finding Roots 200 Find all the roots of the following function and write the function in factored form.

  35. A: Finding Roots 200 Look for: Then use synthetic division.: x = -2, ± 1

  36. Finding Roots 300 Find all the roots of the following function and write the function in factored form without any imaginary numbers.

  37. A: Finding Roots 300 Must be repeated. Look for: Then use synthetic division. x = 3, ± i

  38. Finding Roots 400 Find all the roots of the following function and write the function in factored form without any imaginary numbers.

  39. A: Finding Roots 400 x = -2, 1/3 Look for: Then use synthetic division.: x = - 2, 1/3, ± 3i

  40. Finding Roots 500 Solve:

  41. A: Finding Roots 500 Look for: x = ½ and 5 x Then use synthetic division Then use the quadratic equation x = ½, 5, -3 ± 2i

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