D21 Rational Behavior Assignment - x Rewrite Rational Expressions - Lo x 5 Microsoft Word - rational behavi + X - C wvlearns.k12.wv.us/d21/le/dropbox/301861/576095/DownloadAttachment?fid=4623576 9 20 School Links J Southern West Virg... D2L WV learns C Clever Tool kit Bb Blackboard * e E Microsoft Word - rational behavior ex1.docx 82% + Rational Behavior Assignment 1 1. Consider the following function, f(x)= =x*-6x x2-2x+8 R(x) a. Use polynomial division to write f(x) in the form Q(x) + x2 - 2x+ 8. Where Q(x) is the quotient and R(x) is the remainder. Show your work. R(x) b. What is the second term, x' - 2x +8 getting closer to as x gets larger? R(x) * + 00+ x2 - 2x +8 c. Combining parts a and b, predict what is happening as x -+ cot, f(x) - R(x) Keep in mind f(x) = Q(x) + - x - 2x +8 d. Using algebraic notation, predict what is happening to the function f(x) as x approaches negative infinity. (This will look a lot like part c) O K! Er 1 US $ 0 12:41D21 Rational Behavior Assignment - x Rewrite Rational Expressions - Lo x 5 Microsoft Word - rational behavi + X - C wvlearns.k12.wv.us/d21/le/dropbox/301861/576095/DownloadAttachment?fid=4623576 9 20 School Links J Southern West Virg... D2L WV learns C Clever Tool kit Bb Blackboard * e E Microsoft Word - rational behavior ex1.docx 2 82% + e. What is the y-intercept of the graph? f. Without using a calculator, but using the information we have discovered, sketch an approximate graph of f(x) for -100 % x $ 100 Next Generation Mathematics (7+4) 9 FOR WEST VIRGINIA SCHOOLS 28 71 x . Academic hrovation KI2 Rational Behavior Assignment 1 2. Consider the rational function, R(x) = ; -6x+26 2x3 +4x-6 a. What is happening to R(x) as x gets very large and positive and as x gets very large and negative? (Use correct algebraic notation, refer to 1b) b. Go to Desmos and use a graphing calculator to graph R(x). Take a O K! Er 1 US $ 0 12:41D21 Rational Behavior Assignment - x Rewrite Rational Expressions - Lo x 5 Microsoft Word - rational behavi + X - C wvlearns.k12.wv.us/d21/le/dropbox/301861/576095/DownloadAttachment?fid=4623576 9 20 School Links J Southern West Virg... D2L WV learns C Clever Tool kit Bb Blackboard * e E Microsoft Word - rational behavior ex1.docx 2 / 4 82% + b. Go to Desmos and use a graphing calculator to graph R(x). Take a screen shot and save to submit. Do not delete the graph, we will use it again shortly) 3. We are now going to consider h(x) = _* + 2x + 5x+14 Use polynomial 2x- +4x-6 R(x) division to write h(x) in the form h(x) = Q(x) + 2x' +4x+6' where Q(x) is the quotient and R(x) is the remainder. Show your work. 4. Use your answers to Questions 2 and 3 to figure out what is happening to h(x) as x gets very large and very small. Explain or show how you arrived at your answer. Next Generation Mathematics FOR WEST VIRGINIA SCHOOLS (7+4) 9 O K! Er US $ 0 12:41D21 Rational Behavior Assignment - x Rewrite Rational Expressions - Lo x 5 Microsoft Word - rational behavi + X - C wvlearns.k12.wv.us/d21/le/dropbox/301861/576095/DownloadAttachment?fid=4623576 9 20 School Links J Southern West Virg... D2L WV learns C Clever Tool kit Bb Blackboard * e E Microsoft Word - rational behavior ex1.docx 3 82% + -6x +26 5. Return to your Desmos graph of R(x) = 2x7 + 4x-6. and modify the graph to be -6x+26 2x' +4x-6 2" --1x + 2 . This is now the graph of h(x). 6. On the same graph, add the graph of Q(x) = =x + 2 . Take a screen shot to submit with this assignment. 7. What do you notice? 8. We now consider the function f(x) = _ x + 3x3 -5x3 +4 x + 3x-5 a. Use polynomial division to write f(x) in the form f(x) = Q(x) +- R(x) where D(x) Q, R, and D are the appropriate polynomial functions. (Hint: use x* + 3x3 - 5x3 + 0x + 4 when dividing) O K! US $ 0 12:41D21 Rational Behavior Assignment - x Rewrite Rational Expressions - Lo x 5 Microsoft Word - rational behavi + X - C wvlearns.k12.wv.us/d21/le/dropbox/301861/576095/DownloadAttachment?fid=4623576 9 20 School Links J Southern West Virg... D2L WV learns C Clever Tool kit Bb Blackboard * e E Microsoft Word - rational behavior ex1.docx 4 82% + b. When x gets larger or smaller, what polynomial function will Q(x) most closely resemble? Next Generation Mathematics (7+4) 9 FOR WEST VIRGINIA SCHOOLS 5+ 8 71 x Academic hrovation KI2 Rational Behavior Assignment 1 What can you predict the graph of f(x) will look like as x becomes larger or smaller? Why? d. Using a graphing calculator, graph f(x). Sketch your graph below or take a screen shot. O K! 1 US $ 0 12:41