Precalculus by Richard Wright

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Truthful lips endure forever, but a lying tongue lasts only a moment. Proverbs 12:19 NIV

2-Review

Take this test as you would take a test in class. When you are finished, check your work against the answers.

  1. Simplify
  2. (2 − i) + (−4 + 3i)
  3. (2 − i)(−4 + 3i)
  4. \(\frac{2-i}{-4+3i}\)
  5. Write the equation of the parabola with a maximum at (9, 1) and goes through the point (8, −1).
  6. Describe how the graph of g(x) = 2(x + 3)2 + 4 is transformed from f(x) = x2.
  7. Describe the left and right-hand end behavior of f(x) = x9 − 16x.
  8. Divide with long division (3x3 + 2x − 4) ÷ (3x + 1).
  9. Divide with synthetic division (2x3 + x2 − 3x + 10) ÷ (x − 1).
  10. Use the Factor Theorem to find all the real zeros for the given polynomial function and one factor: x3 + x2 − 14x − 24; x + 2
  11. For the following questions use f(x) = x4 + x3 − 3x2 + 9x − 108.
  12. List all the p's, q's, and possible rational zeros of f(x).
  13. Find all the rational zeros of f(x).
  14. Find the rest of the zeros of f(x) including any complex zeros.
  15. Find a polynomial function with real coefficients that has the following zeros: 1 (with multiplicity 2) and −2 and (2, f(2)) = (2, 8).
  16. Find the intercepts and asymptotes of the following functions.
  17. \(f(x) = \frac{x+3}{x^2-4x+3}\)
  18. \(f(x) = \frac{x^2-64}{x^2-4}\)
  19. \(f(x) = \frac{x^2 + 7x + 12}{x-2}\)
  20. Graph the following functions.
  21. \(f(x) = \frac{x+3}{x^2-4x+3}\)
  22. \(f(x) = \frac{x^2-64}{x^2-4}\)
  23. \(f(x) = \frac{x^2+7x+12}{x-2}\)
  24. Solve the nonlinear inequalities.
  25. x2 + 5x + 9 > 5
  26. \(\frac{x+10}{x-7}+1 ≤ 0\)

Answers

  1. −2 + 2i
  2. −5 + 10i
  3. \(\frac{-11-2i}{25}\)
  4. y = −2(x − 9)2 + 1
  5. Vertical stretch by a factor of 2, shifted left 3 and up 4
  6. Falls to the left, rises to the right
  7. \(x^2-\frac{1}{3}x+\frac{7}{9}+\frac{-43}{9(3x+1)}\)
  8. \(2x^2+3x+\frac{10}{x-1}\)
  9. −3, −2, 4
  10. p = ±1, ±2, ±3, ±4, ±6, ±9, ±12, ±18, ±27, ±36, ±54, ±108
    q = ±1
    p⁄q = ±1, ±2, ±3, ±4, ±6, ±9, ±12, ±18, ±27, ±36, ±54, ±108
  11. −4, 3
  12. ±3i
  13. f(x) = 2x3 − 6x + 4
  14. x-int: −3; y-int: 1; VA: x = 1, 3; HA: y = 0
  15. x-int: −8, 8; y-int: 16; HA: x = −2, 2; HA: y = 1
  16. x-int: −4, −3; y-int: −6; VA: x = 2; SlantA: y = x + 9
  20. (−∞, −4) ∪ (−1, ∞)
  21. [−3⁄2, 7)