Fall 2010 MT1 10

# Fall 2010 MT1 10 - Math 3 Midterm 1 Instructor Nandini...

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Math 3 Midterm 1 10/22/10 Instructor : Nandini Bhattacharya Use of books, notes and graphing utilities is not permitted on this exam. Show all your work to get partial credit. Your Name: -------------------------------------------------- Student id#-------------------------------------------------- Your TA -------------------------------------------------- Max Possible Your score Problem 1: 20 Problem 2: 20 Problem 3: 15 Problem 4: 15 Problem 5: 20 Problem 6: 10 TOTAL: 100 1. (20 points) Give a decent sketch of the graph of the following functions. Please include all the information indicated under each part and don’t forget to carefully graph the functions at those points.

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a)(10 points) f ( x ) = -3x 2 + 12 ξ x-intercept(s): y-intercept: Coordinates of the vertex By completing the square: Check your answer from above by using the vertex formula: Graph: Axis of symmetry b) (5 points) f ( x ) = (ξ-3 29 (ξ+ 2 29 (ξ+ 1 29 x-intercept(s): y-intercept:
Graph: c) (5 points) f ( x ) = 2 - 2 x-intercept(s): y-intercept: Graph: Equation of the asymptote: 2. (20 points) Consider the function f ( x ) = (ξ-3 29 -1 a) Find the domain and range of f ( x )

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b) Show that the function f(x) has an inverse. Hint: You can show this either algebraically or graphically.
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