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# 71 - Department of Mathematics The City College of New York...

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Department of Mathematics The City College of New York Mathematics 19500 Final Examination December 2005 Instructions: Show all work. Calculators are not permitted. Please answer: 12 questions from Part I (5 points each) 5 questions from Part II (5 points each) 2 questions from Part III (7.5 points each). Make sure to number each problem clearly in your answer book Draw a box around each answer. Cross out all scratch work. Part I: Algebra and functions. Answer any 12 questions (5 points each) 1 . Find equations of a) the vertical line through (2, 8) and b) the horizontal line through (2, 8). 2. Find an equation of the straight line through the point (-3,7) that is parallel to the line with equation . 2 4 + = y x 3. Solve the inequality 12 5 1 + x . Write your answer in interval form. 4. Solve the inequality . Write your answer using inequalities. 12 2 + < x x 5. Given and , find and simplify . 2 3 6 7 ) ( x x x f = x x g = 2 ) ( )) ( ( x g f 6. Given 3 ) ( + = x x x f , find the inverse function . ) ( 1 x f 7 . Given , find and simplify 2 ) ( x x x f = h x f h

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