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PastExams - Common Exam 1 Solution MATH 111-015 September...

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Unformatted text preview: Common Exam 1 Solution MATH 111-015 September 21, 2005 Please report any error to fp2@njit.edu 1. (15 Points) Let the function f ( x ) be defined as f ( x ) = x + 2- 1 x < 1 2 1 x 3 (a) Sketch the graph of this function. (b) Find the domain and the range of this function. (c) Is this a one-to-one function? Explain. Solution : (a) The graph of the given function is shown in figure(??). ! 3 ! 2 ! 1 1 2 3 4 5 ! 1 1 2 3 4 5 x f(x) Figure 1: This is the graph of the function of exercise 1. (b) From the graph and the definition of f ( x ) we deduce that the domain of the function is: D = [- 1 , 3] , while its range is: [1 , 3] (c) No, this function is not one-to-one since it fails the Horizontal Line Test as we can see from the graph. 2. (15 Points) Let f ( x ) = 1- 3 x- 2 : (a) What kind of a function is f ( x ) (linear, polynomial, algebraic, trigonometric, exponential, logarithmic)?Is this and odd function? An even function? A decreasing function? An increasing function? (b) What is the natural domain of definition of this function? 1 (c) Graph this function, not by plotting the points, but by starting with a graph of one standard functions and then applying appropiate transformations. State clearly which transforma- tions you used. Solution : (a) This is an algebraic function, from the graph we can also see that its neither even or odd. However we can notice from its graph that it is a decreasing function (and therefore it is not increasing)....
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This note was uploaded on 04/07/2008 for the course MATH 111 taught by Professor ? during the Spring '05 term at NJIT.

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PastExams - Common Exam 1 Solution MATH 111-015 September...

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