74 - Department of Mathematics Mathematics 19500 The City...

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Department of Mathematics The City College of New York Mathematics 19500 Final Examination Spring 2006 Instructions: Do 13 questions from Part I and 5 questions from Part II. Show all work. Calculators are not permitted . Part I. Answer any 13 questions (5 points each) 1. A parabola has equation . Find the co-ordinates of the parabola’s intercepts and vertex and sketch its graph. 5 6 2 + = x x y 2. Find an equation of the straight line through the point (-4, 7) that is perpendicular to the line with equation 2 x + 3 y = 5 . 3. Sketch the graph of . Find all intercepts and asymptotes and label them clearly on your graph. 3 2 + = x e y 4. Solve the inequality 12 3 1 x . Write your answer in interval form. 5. Given , find and simplify 2 2 ) ( 2 + = x x x f h x f h x f ) ( ) ( + . 6. Given x x x f = 1 1 ) ( 2 and ; find and simplify 2 ) ( + = x x g ) 2 ( )) ( ( f x g f 7. Find the inverse of the function x x x f = 1 3 2 ) (. 8. The length of a rectangle is x . Its area is 50 square inches. Find a formula for its perimeter in the form ______ . = ) ( x f 9.

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74 - Department of Mathematics Mathematics 19500 The City...

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