MATH 2412 Precalculus

North Lake College

David Katz, instructor

Section by Section List of Test Topics For Exam #1 (Chapters 2-3)

The exam will consist of 10 multiple-choice questions from this list of 65 topics from your homework sections.

  1. (2-1) Evaluate a function given a numeric input, e.g., evaluate f(-4)

  2. (2-1) Evaluate a function given a variable expression as input, e.g., evaluate: f(x+h)
  3. (2-1) Evaluate a piecewise defined function for an indicated value
  4. (2-1) Know how to evaluate and graph an absolute value function
  5. (2-1) Determine the difference quotient for a given function (cf. #29-34 on p.152)
  6. (2-1) Evaluate a function used in an applied problem
  7. (2-1) Determine the domain of polynomial function
  8. (2-1) Determine the domain of a radical function
  9. (2-2) Determine whether a graph represents a function
  10. (2-2) Determine whether an equation in x and y represents a function
  11. (2-2) Sketch the graph of a piecewise defined function
  12. (2-2) Given two points, create a linear function that passes through those points
  13. (2-3) Express a statement about direct variation or direct proportion as a formula
  14. (2-3) Express a statement about inverse variation or inverse proportion as a formula
  15. (2-3) Express a statement about joint variation as a formula
  16. (2-3) Use given information to solve for the constant of proportionality
  17. (2-4) Compute the average rate of change of a function between two given values of the variable
  18. (2-4) Estimate the average rate of change using the graph of a function
  19. (2-4) Compute the average rate of change using a table of values
  20. (2-5) Given a function, use a transformation to graph a vertical shift up or down
  21. (2-5) Given a function, use a transformation to graph a horizontal shift left or right
  22. (2-5) Given a function, use a transformation to graph a reflection about the line x = 0
  23. (2-5) Given a function, use a transformation to graph a reflection about the line y = 0
  24. (2-5) Perform multiple transformations on a single function
  25. (2-5) Determine whether a function is odd, even, or neither
  26. (2-6) Determine the x-intercepts (if any) and y-intercept of the graph of a parabola function
  27. (2-6) Determine the coordinates of the vertex of a parabola function
  28. (2-6) Determine if a the graph of a parabola function opens up or down
  29. (2-6) Compute the maximum or minimum of a quadratic function
  30. (2-7) Know basic area and perimeter formulas for a rectangle, triangle, and circle
  31. (2-7) Create a function to model an applied problem in geometry
  32. (2-8) Add, subtract, multiple, or divide two functions
  33. (2-8) Determine the domain of the sum, difference, product, or quotient of two functions
  34. (2-8) Compute the composite of two or more functions given the function formulas
  35. (2-8) Compute the composite of two or more functions given the graphs of the functions
  36. (2-8) Determine the domain of the composite of two or more functions
  37. (2-8) Use composite functions to model applied problems
  38. (2-9) Classify a function as one-to-one (aka injection) based on its graph (hint: use horizontal line test)
  39. (2-9) Classify a function as one-to-one based on its formula
  40. (2-9) Given two functions, determine analytically whether they are inverses of each other
  41. (2-9) Given the graphs of two functions, determine whether they are inverses of each other (hint: reflect about y = x)
  42. (2-9) Compute the inverse function of a one-to-one function: (hint: interchange x with y and solve for y)
  43. (2-9) Specify the domain and range of a function and its inverse
  44. (3-1) Given a polynomial in factored form, determine all x-intercepts (if any)
  45. (3-1) Given a polynomial function, determine its end behavior
  46. (3-1) Given a polynomial, determine the y-intercept
  47. (3-2) Divide two polynomials using long division
  48. (3-2) Use the Factor Theorem to show that a given value is a zero of the polynomial
  49. (3-2) Given the zeros and degree of a polynomial, write a polynomial in factored form
  50. (3-3) Determine all rational zeros of a polynomial using the Rational Zeros Theorem
  51. (3-3) Determine all real zeros of a polynomial using the Rational Zeros Theorem, long division, and quadratic formula
  52. (3-3) Compute the upper and lower bounds for the real zeros of a polynomial
  53. (3-4) Know how to add, subtract, multiply, and divide two complex numbers
  54. (3-4) Determine the solutions (real or complex) of a quadratic equation
  55. (3-4) Substitute the real or complex solution back into the quadratic equation to check
  56. (3-5) Factor a polynomial and state the multiplicity of its factors
  57. (3-5) Given the degree of a polynomial and its zeros of specified multiplicity, write the polynomial in factored form
  58. (3-5) Know how to use the Complex Conjugate Zeros Theorem
  59. (3-5) Know what the Fundamental Theorem of Algebra means (i.e., a polynomial of degree n had n factors)
  60. (3-5) Compute the zeros (real and/or complex) of a polynomial
  61. (3-6) State the domain of a rational function
  62. (3-6) Determine the vertical asymptote lines of a rational function (if any)
  63. (3-6) Determine the horizontal asymptote line of a rational function (if one exists)
  64. (3-6) Determine the slant asymptote line of a rational function (if one exists)
  65. (3-6) Sketch the graph of a rational function
 

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