College Algebra MATH 1314 or MATH 1414

David Katz, instructor

Section by Section List of Test Topics for Exam #2 (Chapter 3) from College Algebra by Robert Blitzer (4th edition)

The exam will consist of 10 multiple-choice questions from this list of topics from your homework sections.

Note: you will be required to know by memory the formulas of this unit except following, which will be given to you when you take the exam:

 

Turning points < n – 1             If n = m, then y = a/b             If n < m, then y = 0

  1. (3.1) Identify the vertex of a parabola from its graph
  2. (3.1) Identify the coordinates of the vertex of a quadratic function in standard form, i.e., the vertex of y = a(x–h)2+ k is at (h,k)
  3. (3.1) Identify the coordinates of the vertex of a quadratic function in general form, i.e., the x-coordinate of the vertex of y = ax2+bx+c is at –b/(2a)
  4. (3.1) Determine if the graph of a quadratic function opens up or down by examining the leading coefficient
  5. (3.1) Determine if the graph of a quadratic function has a minimum or maximum point by examining the leading coefficient
  6. (3.1) Use the vertex of a quadratic function’s graph to determine the minimum or maximum value for that function
  7. (3.1) Use the vertex of a quadratic function’s graph to determine the axis of symmetry for that graph
  8. (3.1) Solve applied problems using the minimum or maximum of a quadratic function
  9. (3.2) Classify functions as polynomial or non-polynomial
  10. (3.2) Be able to factor four-term polynomials by grouping method when possible
  11. (3.2) Determine the end behavior of a polynomial function’s graph by examining the degree and leading coefficient of the function
  12. (3.2) Understand how linear factors of a polynomial correspond to zeros of the polynomial and vice versa (aka the Factor Theorem)
  13. (3.2) Identify the degree of a polynomial in standard form; e.g., the degree of p(x) = 4x3+2.5x–10 is 3
  14. (3.2) Identify the degree of a polynomial in factored form; e.g., the degree of p(x) = 5(x–2)3(x–10) is 4
  15. (3.2) Given a polynomial in factored form, identify the multiplicity of each factor and zero
  16. (3.2) Know that zeros of even multiplicity correspond to x-intercepts that touch the x-axis
  17. (3.2) Know that zeros of odd multiplicity correspond to x-intercepts that cross the x-axis
  18. (3.2) Know that all x-intercepts are also zeros, but not all zeros are x-intercepts
  19. (3.2) Know that the max number of turning points (hills and valleys) in a graph = n – 1, where n is the degree
  20. (3.2) Use your knowledge of zeros, turning points, and end behavior to draw a quick sketch of a polynomial
  21. (3.2  Locate the y-intercept of a polynomial function
  22. (3.2) Be able to check your sketches of polynomials with a  graphing calculator
  23. (3.3) Perform synthetic division of polynomials
  24. (3.3) Understand how synthetic division is a quick way to evaluate a polynomial for a given x-value
  25. (3.4) Use the Rational Zeros Theorem to list all possible rational zeros of a polynomial
  26. (3.4) Use synthetic division of polynomials to find additional factors of a polynomial
  27. (3.4) Use a graphing calculator to determine the number of positive and negative zeros
  28. (3.4) Know that a corollary to the Fundamental Theorem of Algebra states that the degree of the polynomial = number of zeros or linear factors
  29. (3.4) Use Rational Zeros Theorem and synthetic division to completely factor or solve a polynomial
  30. (3.4) Given the zeros of a polynomial, write the polynomial in factored form
  31. (3.4) Use the Conjugate Zeros Theorem to find complex zeros of a polynomial
  32. (3.5) Determine the domain of a rational function
  33. (3.5) Be able to find the y-intercept, if one exists, of a rational function
  34. (3.5) Determine the vertical asymptotes, if any, of a rational function (don’t forget to simplify and cancel common factors first!)
  35. (3.5) Identify the horizontal asymptote, if one exists, of a rational function
  36. (3.5) Identify the slant asymptote line, if one exists, of a rational function
  37. (3.5) Use your understanding of asymptotes, intercepts, and the graphing calculator to draw a quick sketch of a rational function’s graph
  38. (3.6) Solve polynomial inequalities
  39. (3.6) Solve rational inequalities

 

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