Math 3304 Basics Homework HOLLYER Name You are encouraged to work together on problems sharing ideas and hopefully arguing your way through Please give credit where it is due though if someone s email or post helped you out Keep your answers in order and work on the front side only If you need to insert additional pages then put them in the proper order Please work neatly if it s illegible then the grader has instructions to award a zero on that work This is a 145 point assignment 10 of these points are neatness points to be awarded at the grader s discretion see above Be neat and legible please Don t skimp on paper it needs to be easy to grade This assignment is due by noon on the Monday listed in the course calendar on my website No late homework will be accepted for any reason Please submit the homework in a single pdf file to the assignments tab in your courseware accout GRADE Work 135 Neatness 10 Total 1 12 points 4 for A 8 for B 1 A Let A be the set of all real numbers Let B also be the set of all real numbers What is the resulting set for A B Sketch the picture framework B Let A 0 1 2 3 4 B x x is an even natural number C x 1 x 6 x is a real number and D x x 0 x is a multiple of 3 and is a natural number A B A C C D B C A 2 Problem 2 32 points total 8 each part 3 list 2 graph 2 bounds 2A Given 1 n is a natural number n Give a list of set elements that is at least 6 elements long Use appropriate notation Make a 2 D graph of this set showing at least 6 point pairs Discuss the bounds Where is the set bounded or unbounded Include a sentence indicating HOW you know this If there is a glb or a lub be sure to label it clearly 3 2B n Given 10 n is a natural number Give a list of set elements that is at least 6 elements long Use appropriate notation Make a 2 D graph of this set showing at least 6 point pairs Discuss the bounds Where is the set bounded or unbounded Include a sentence indicating HOW you know this If there is a glb or a lub be sure to label it clearly 4 2C n Given 2 n is a natural number Give a list of set elements that is at least 6 elements long Use appropriate notation Make a 2 D graph of this set showing at least 6 point pairs Discuss the bounds Where is the set bounded or unbounded Include a sentence indicating HOW you know this If there is a glb or a lub be sure to label it clearly 5 2D n 1 Given n 1 n is a natural number Give a list of set elements that is at least 6 elements long Use appropriate notation Make a 2 D graph of this set showing at least 6 point pairs Discuss the bounds Where is the set bounded or unbounded Include a sentence indicating HOW you know this If there is a glb or a lub be sure to label it clearly 6 3 Find the domain x intercept s and y intercepts for the following functions 48 points 6 points each part 2 per answer a 1 1 f x x 3 2 Domain Work x intercept Work y intercept Work 7 b f x x 2 x 6 Domain Work x intercept Work y intercept Work 8 c f x 1 2 x 18 Domain Work x intercept Work y intercept Work 9 d f x 5x 3 125 Domain Work x intercept Work y intercept Work 10 e f x 2x 36 x 9 Domain Work x intercept Work y intercept Work 11 f f x 9 3x Domain Work x intercept Work y intercept Work 12 g f x 1 2x x 3 2 Domain Work x intercept Work y intercept Work 13 h f x 1 6 x 11x 3 2 Domain Work x intercept Work y intercept Work 14 4 points Evaluate the following functions for the given x value List the domain and the range on the sketch in interval notation Label any asymptotes or state that there are none Sketch the graph Feel free to use a graphing calculator or program MathGV is a nice program and it s free 4A 8 points f x 3 x f 1 f 0 f 1 2 Domain Range Sketch 2 points Asymptotes 15 4B 8 points f x x x 2 f 1 f 0 f 1 2 Domain Range Sketch 2 points Asymptotes 16 4C 9 points f x x 2 1 f 1 f 0 f 1 2 f Domain Range Sketch 2 points Asymptotes 17 4D 9 points f x 8 x f 1 f 0 f 1 3 f 1 2 Domain Range Sketch 2 points Asymptotes 18 4E 9 points f x x 3 2x 2 5x 6 hint x 1 is a factor Factored form f 1 f 0 f 1 2 Domain Range Sketch 2 points Asy 19