Rajat Gupta

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Module 3 Written Assignment: Part 3

General Expectations: (i). For full credit, your written assignments must be accompanied by a narrative explanation/rationale for the process that you used to solve each problem. How did you choose the steps? What is the logic behind the choices that you made? Explain why the problems were solved the way they were solved. Use complete sentences, good English, and proper mathematical notation. (ii). For full credit, your written assignments must include the statement of each problem so the reader knows what you are trying to demonstrate. In cases where the assignment refers you to a book problem, you must also copy the statement of the appropriate problem in the book. Note: Be sure to do the practice exercises in this assignment. They have been carefully chosen to help you understand the material needed to do the assigned exercises that immediately follow.

Section 3.1: Practice: Do # 1a and 1c from Section 3.1. Check your answers in the back of the book. 1. Let f = {(Mindy, Subaru), (Jasmine, Toyota), (Sharon, VW), (Roger, Kia), (Jose, VW)}. (a.) What is the domain of this relation? (b.) What is the range? (c.) Is this a function? Why or why not? (d.) Is this relation one-to-one? Why or why not? (d.) Define g as {(Mindy, Subaru), (Jasmine, Toyota), (Sharon, VW), (Roger, Kia), (Jose, Oldsmobile)}. Is g a one-to-one function? Why or why not? 2. Prove that the function f : R → R given by f (x) = 4x − 3 is surjective. [You may use the Proof Shuffler applet to help you]. 3. Prove that the function f : [0, ∞) → [4, ∞) given by f (x) = x2 + 4 is bijective. [You may use the Proof Shuffler applet to help you]. 4. Let f = {(2, 1), (2, 2), (2, 3), (4, 4)}. Is this a function? Why or why not? 5. Define f to be a function from R to R by f (x) = x2 + 1. (a.) Is f injective? Explain your answer. (b.) Is f surjective? Explain your answer. 6. Give…...

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