Homework 6 – 38 questions

Homework 6 – 38 questions
Week 6 questions 3.2 – zeros of polynomial functions – refer to the pdf for each section of questions. 3.3 – The theory of equations 3.4 – Graphs of Polynomial Functions 3.5 Rational Functions and Inequalities
Homework 6 – 38 questions
Homework Assignment week 6 Due July 12 th, 2022 The following homework assignment consists of exercises from sections 3.2 , 3.3, 3.4 and 3.5 in the textbook. There are 32 assigned exercises, and y ou are asked to complete all of them for full credit on the assignment. Each exercise is worth 3 points for a total of 96 points . There are 6 extra credit exercises listed in the section s as well. Each extra credit exercise is worth 3 points for a total of 18 extra credit points . Please see the rubr ic on homework assignment week 1 for grading details on this homework assignment. I recommend working on the homework exercises as soon as possible after our class meetings where we discuss the topics . You may h and write or type the weekly assignments, and turn in during our class meeting or submit your work in the assignment section of the D2L shell as one complete pdf, by the due date. You must show all work for full or partial credit, using the methods that we discuss in our class meetings. Please submit organized, legible and complete work. Section 3.2 (pgs. 288 -289) *See a hint/guide for exercises 13,15, 27, 29, 41, and 43 on page 2 of this assignment . Exercises 49, 51, and 57, 59 are the sam e polynomials. You will find the possible zeros of the polynomials in HW exercises 49 and 51, and check the possible zeros exercises 57 and 59. Exercise 13 Exercise 15 Exercise 27 Exercise 29 Exercise 41 Exercise 43 Exercise 49 Exercise 57 Exercise 51 Exercise 59 Homework Assignment week 6 , page 2 Section 3.2 continued (pgs. 288 -289) Hint/guide for exercises 13,15, 27, 29, 41 and 43. Exercise 13: Find the quotient and remainder when the first polynomial is divided by the second. 2+ 4+ 1, − 2 Step 1: Since − 2 is the factor ℎ → − 2= 0 → = 2 → 2 is the zero (or solution). Step 2: synthetic division Step 3: Find the quotient and remainder 2 1 4 1 Step 4: Fill in the blank: Also notice that, ()= 2+ 4+ 1, so (2)= 22+ 4(2)+ 1= _____= . Use the above as a guide for exercises 15, 41 and 43. For exercise 15, the quotient is ____2+ ____+ ____. For exercises 41 and 43, step 1 is already done. Section 3.3 (pg . 298) Exercise 9 Extra Credit: Exercise 13 Exercise 17 Exercise 21 Exercise 25 Exercise 29 Extra credit: Exercise 35 Exercise 45 Exercise 47 Extra credit Exercise 51 The 2 digits in blue are the coefficients of the quotient. ____+ ____ The digit in orange is the remainder, = _______ Homework Assignment week 6 , page 3 Section 3.4 (pgs. 310 -312) *For exercises 67, 69, and 71 do steps 1 -6 below and on page 4 of this assignment . Exercise 9 Exercise 27 Exercise 33 Exercise 67 Exercise 69 Exercise 71 Exercise 97 Exercise 103 Sect ion 3.4 (pgs. 310 -312) For HW exercises 67,69 and 71 do steps 1 -6 below. Strategy for Graphing a Polynomial Function (page 306): (1) Check for symmetry (by finding (−)) If (−)= (), then the graph of a function is symmetric about the y -axis and is an even function If (−)= −(), then the graph of a function is symmetric about the origin and is an odd function If the graph is a quadratic function, then it is symmetric about its axis of symmetry , = −/(2) (2) Find all real zeros of the polynomial function (set polynomial equal to zero and solve for . Try factoring first or use the methods of section 3.2) The zeros are the x -intercepts in step 3 (3) Determine the behavior at the corresponding x -intercepts . The zeros from step 2 are the intercepts. If the root has odd multiplicity, then the graph crosses the x -axis at the x -intercept. If the root has even multiplicity, then the graph touches but does not cross the x -axis at the x -intercept . (4) Determine the behavior as → ∞ and → −∞ (by checking the degree and leading coefficient of the polynomial function). You may use the language that the fun ction “goes right/left and up/down” If the degree is odd and the LC is greater than 0 , then as → ∞, ()→ ∞ and as → −∞, ()→ −∞ If the degree is odd and the LC is less than 0 , then as → ∞, ()→ −∞ and as → −∞, ()→ ∞. If the degree is even and the LC is greater than 0 , then as → ∞, ()→ ∞ and as → −∞, ()→ ∞ If the degree is even and the LC is less than 0 , then as → ∞, ()→ −∞ and as → −∞, ()→ −∞. (5) Calculate several ordered pairs including the y -intercept . To calculate the y-intercept, let = 0 and solve for . Then, we generally have enough points to graph, but you can find and graph more. (6) Draw a smooth curve through the points to make the graph . Graph the x -intercepts from step 2, and the y -intercept from step 5. Use the results from step 1, step 3 and step 4 to draw a smooth curve. Homework Assignment week 6 , page 4 Sect ion 3.4 continued (pgs. 310 -312) For HW exercises 67,69 and 71 do steps 1 -6 below. For hom ework exercises 67, 69 and 71, o rganize your findings in the following way. Section 3.5 (pgs. 327 -328) *For exercises 37 and 41, do steps 1 -5 below and page 5 of this assignment . Exercise 23 Exercise 27 Exercise 31 Exercise 37 Exercise 41 Extra credit: Exercise 63 Extra Credit: Exercise 83 Exercise 85 Exercise 103 Extra Credit: Exercise 105 (1) Symmetry:__________________________ (2) zeros_______________ x -intercepts ______________ (3) For each x -intercept fill in the blanks of the following at_______the graph ____________ the x -axis (4) as → ∞, ()→ ________ and as → −∞, ()→ _______ or as the graph goes to the right, it also goes ________ and as the graph goes to the left, it also goes_________. (5) y-intercept______________ (other points______________) Homework Assignment week 6 , page 4 Section 3.5 (pgs. 327 -328) For homework exercises 37 and 41, do the following 5 steps. Graphing Rational Expressions (pg. 319): (1) Determine the asymptotes and draw them as dashed lines . The vertical asymptote(s) : set the denominator equal to zero and solve for the line(s) = . The horizontal or oblique asymptote (s): If the degree of () is less than the degree of (), then the line = 0 is the horizontal asymptote (the x -axis is the horizontal asymptote). If the degree of () is equal to the degree of (), then the horizontal asymptote is determined by the ratio of the leading coefficients. If the degree of () is greater than the degree of (), the n the oblique asymptote is the line = (use synthetic division to find the quotient) (2) Check for symmetry (we will omit this step) (3) Find any intercepts (There may not be a ny x -intercepts or y -intercepts because of the asymptotes) To find the x -intercept(s) let = 0 and solve for . To find the y -intercept(s) let = 0 and solve for . (4) Plot several selected points to determine how the graph a pproaches the asymptotes . (You will need at least two points on both sides of the vertical asymptote.) Construct a T -table, choose x values and find the corresponding y values. (5) Draw curves through the selected points, approaching the asymptotes . (1) Asymptotes: __________________________ (2) symmetry_(omit this step)______________________ (3) Intercepts:________________________ (4) T-table determining several points