3 Pages

# practice-final

Course Number: MATH 140, Fall 2008

College/University: Iowa State

Word Count: 484

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Math 140 E (Sp09) PRACTICE TEST FOR FINAL Suggestion: Try to solve it like a real test without notes and text and calculator within 2 hours. Later you can compare your answer with solutions. Try to explain every details. You may think you are explaining how to solve those questions to somebody who doesn't know about the college algebra. 1. Answer the following questions. a. Find an equation of the line...

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140 Math E (Sp09) PRACTICE TEST FOR FINAL Suggestion: Try to solve it like a real test without notes and text and calculator within 2 hours. Later you can compare your answer with solutions. Try to explain every details. You may think you are explaining how to solve those questions to somebody who doesn't know about the college algebra. 1. Answer the following questions. a. Find an equation of the line containing the point (-1, 2) that is perpendicular to the line y = 2x. b. Find an equation of the line containing the points (-3, 4) and (2, 5). 2. Two functions are given by f (x) = x + 1 and g(x) = 3x. Answer the following questions. When you state domains, use interval notations. a. Find domains of f and g. b. Evaluate (f + g)(3) and (f /g)(3). c. Evaluate (f f )(8) and (g f )(15). d. Find (f g)(x) and the domain. 3. Determine whether f (x) = -2x2 + 3 is even, odd, or neither (Explain why). 4. Write an each expression in the standard form a + bi where a, b are real numbers. a. i20 + i23 + i25 + i27 . b. 2 - 3i . 2-i 5. Solve |5 - 6x| < 9. 6. For the quadratic function f (x) = 4x2 - 2x - 1: a. Determine whether the parabola defined by f (x) is open up or down (explain why). b. Find the vertex and axis of symmetry of f (x). c. Find the x-intercepts of f (x). 7. a. Write a factored form of polynomial which has zeros -2, 1, 1, 3, -5. b. Find a polynomial function degree of 4 with rational coefficients and that has 3 - i and 5 as two of its zeros. 8. For the polynomial function f (x) = x3 + 2x2 - 5x - 6: 1 2 a. List the potential rational zeros of f (x). b. Write f (x) in linearly factored form. 9. For the polynomial function h(x) = (x - 1)2 (x - 3): a. Find the leading term and determine the end behavior h(x). b. Find all intercepts of h(x) c. Graph h(x). 10. For the rational function 2x - 1 , x+2 Find all asymptotes of R(x) and all intercepts of R(x). Also graph R(x) (Clearly.) R(x) = 11. The function 2x + 1 ,x = 1 x-1 is one-to-one. Find its inverse and figure out (f f -1 )(x). f (x) = 12. Graph f (x) = -ex-3 by using the basic exponential graph of y = ex . Describe how to get the graph of f from the graph of y = ex . Determine the domain, range, and horizontal asymptote of f . (Question: What if you have g(x) = - ln(x - 3) ?? ) 13. Solve 2x 8-x = 4x . 2 14. Solve log4 (x + 3) + log4 (2 - x) = 1. 15. Find the exact value of log5 3 25. 16. Evaluate 4 k!. k=0 17. The eighth term of an arithmetic sequence is 75, and the twentieth term is 39. Find the 1001th term. 3 18. Find 1 + 3 + 5 + + 59. 19. Find the fifth term and the general term of the geometric sequence which is given by 6 18 2, , , . . . . 5 25 20. Evaluate 5 k=0 1 4 k . 21. Find the coefficients of x3 and x7 in the expansion of (2x - 1)12 .