PracticeFinalExam

PracticeFinalExam - } . (a) Show that the relation R has an...

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MAP 103: Proficiency Algebra — Final Exam Answer 10 questions at 10 points each. Show all work. 1. Let A = { 0 , } and B = { 1 , 2 } . (a) Compute the sets A B and A B. (b) Find | A B | + | A B | . 2. A number X has the formula X = 2 A + 3 B + 4 C - 1 2 C + 1 3 B - 1 4 A. Find the value of X when A = - 1 ,B = 1 ,C = 2 . 3. Consider the linear inequality 3 2 (4 x - 8) 6 1 2 (2 x - 2) + 3 4 (4 + 4 x ) . (a) Find and graph the solution set. (b) On the interval [ - 2 , 4] , what is the smallest interval containing the least number of solu- tions to the given inequality? 4. Consider the line y = - x - 1 . (a) Find the equation of the line that is parallel to the given line and contains the point ( - 1 , 1) in slope-intercept form. (b) Find the equation of the line that is perpendicular to the given line and contains the point (1 , - 1) in the slope-intercept form. 5. Consider the quadratic equation p ( x ) = 2 x 2 + 3 x - 4 . (a) Describe the nature of the roots. (b) If the graph of p ( x ) intersects the line y = - x +1 , what are the coordinates for the points of intersection? Justify your answer graphically and algebraically. 6. Consider the relation R = { (1 , 0) , (2 , ln 2) , (3 , ln 3) , (4 , 2 ln 2)
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Unformatted text preview: } . (a) Show that the relation R has an inverse R-1 . (b) Find the equation for the inverse function f ( x ) given by R-1 and compute f (0) . 7. Let f ( x ) = ( x + 1) 2 + 1 and g ( x ) = x 2 . (a) Find the composition h ( x ) = g-1 f-1 ( x ) . (b) What is the domain of h ( x )? 8. Let z = 1 2 + 3 2 i . (a) Find z and show that z z = 1 . (b) If w = 1-i , nd in simplest x + i y form the ratio = z w . 9. (a) Solve for x and check: 3 x-10 3-x =-9 . (b) After 4 years, 12 grams of a certain element decays to half of its original amount. If the equation A ( t ) = Pe kt can be used to the model the rate of decay, nd the value of the decay constant k. Show all work. 10. (a) Solve for x : 1 2 ln(2 x )-ln(3 x ) = 0 . (b) Let h ( x ) = ln( e x 2 +1 + 1) + 1 . Find two functions f ( x ) and g ( x ) such that h ( x ) = f g ( x ) . What are the domains of f ( x ) and g ( x ) , respectively?...
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This note was uploaded on 04/18/2010 for the course MAP 103 taught by Professor Staff during the Fall '08 term at SUNY Stony Brook.

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PracticeFinalExam - } . (a) Show that the relation R has an...

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