Oblique Asymptotes

Question 1 The rational function below has an oblique asymptote. Determine the value of k. Not yet answered f(x) = 15x8+ 10x3-3x2+1 11xk - 2x2 +6 Points out of 12.50 Select one: O a. 9 O b. 6 O c. 10 O d. 7Information For questions 2 - 4, determine whether the given function has an oblique asymptote. Question 2 Not yet answered Points out of 12.50 Select one: O a. yes, there is an oblique asymptote O b. no, there is not an oblique asymptoteQuestion 3 Not yet answered Points out of 12.50 Select one: O a. yes, there is an oblique asymptote O b. no, there is not an oblique asymptoteQuestion 4 Not yet answered Points out of 12.50 Select one: O a. yes, there is an oblique asymptote O b. no, there is not an oblique asymptoteInformation For questions 5 - 8, determine whether each rational function has an oblique or horizontal asymptote. Then, write the equation of the asymptote. Question 5 h ( x ) = X5 - 7x2-6 Not yet x2 -2x-15 answered Points out of Select one: 12.50 O a. The oblique asymptote is y = x - 5. O b. The oblique asymptote is y = x - 7. O c. The horizontal asymptote is y = 0. O d. The horizontal asymptote is y = 1. O e. The horizontal asymptote is y = 6 15Question 6 f(x) = 4x + 7x+ 1 Not yet 8x6 -3x-4 answered Points out of Select one: 12.50 O a. The horizontal asymptote is y = - - 1 - 4 O b. The horizontal asymptote is y = 2 O c. The horizontal asymptote is y = 0. O d. The oblique asymptote is y = 2x. O e. The oblique asymptote is y = =X-1. 1 Question 7 9(x) = 12x-5x+ 30 Not yet 2x3 + 7x-1 answered Points out of Select one: 12.50 O a. The horizontal asymptote is y = 0. O b. The horizontal asymptote is y = 6. O c. The oblique asymptote is y = x - 3. O d. The horizontal asymptote is y = 6 O e. The oblique asymptote is y = 6x + 5.Question 8 g(x) = 7x2 +5x+3 Not yet x+2 answered Points out of Select one: 12.50 O a. The horizontal asymptote is y = 3 N O b. The horizontal asymptote is y = 0. O c. The horizontal asymptote is y = 7x + 5. O d. The oblique asymptote is y = 7x - 9. O e. The oblique asymptote is y = 7.\fQuestion 1 Conduct a sign test to find the behavior of the graph as x gets close to the vertical asymptote(s). Drag and drop the values and the Not yet + and - symbols to complete the table. Place numbers from lowest to highest answered Points out of Sign of Each 20.00 Factor Sign of Function + -3.001 -2.999 2.999 3.001 3.999 4.001 4.999 5.001 EInformation For questions 2 - 3, fill in the blank to describe the behavior of the graph around the indicated vertical asymptote. Question 2 When the value of x is to the left of, but close to the rightmost vertical asymptote, then the graph is the x-axis and y Not yet answered approaches infinity. Points out of positive negative above below 20.00 Question 3 When the value of x is to the right of, but close to the leftmost vertical asymptote, then the graph is the x-axis and y Not yet answered approaches infinity. Points out of positive negative above below 20.00Question 4 Use your work from questions 1 - 3 to determine which of the following graphs represents the rational function below. Not yet 4x answered f ( x) = (x-3)(x+3) Points out of 20.00 Select one: O a. O b. O c.Lesson: Graphs of Rational Functions by HandQuestion 5 For the function below, use a sign test to find the behavior of the graph as x gets close to the vertical asymptote(s). Then, use the Not yet results to determine which of the following graphs represent the function. answered Points out of f ( x ) = -3x 20.00 ( x - 1) 2 ( x + 2 ) 2 Select one: O a . O b.\fAssignment: Graphs of Rational Functions by Hand For questions 1 -7, use the rational function below. 8(x + 2) (x - 3) (x+ 1) f ( x ) = 2(x - 1) (x + 2)(x+4) 1. Identify the hole(s) and vertical asymptote(s) of the function. 2. Conduct a sign test to find the behavior of the graph as x gets close to the vertical asymptote(s). 3. Identify any horizontal or oblique asymptotes of the function. 4. Fill in the blanks to describe the end behavior of the graph. As x - -0o, y - As x - 00, y - 5. Find the zero(s) of the function. 6. Find the y-intercept of the function. 7. Use your work from questions 1 - 6 to sketch the graph of the rational function.Information For questions 1 - 2, use the following: A television costs $700. If the annual cost for the electricity to run the television is $20, then the annual cost of running the television each year is given by the rational function C(x) = 100 + 20x where x is the number of X years since the television was purchased. Question 1 The annual cost of running the television is $160. Which rational equation can be used to find how long has it been since the Not yet television was purchased? answered Points out of Select one: 20.00 O a. 160 = 700 + 160 160 O b. c(160) = 700+ 20(160) 160 O c. . 160 = 700+ 20x X O d. 160 = 700+ 20x Question 2 Solve the equation from problem 1 to find when the annual cost of running the television is $160. Not yet answered Select one: Points out of O a. 7 years 20.00 O b. 5 years O c. 10 years O d. 15 yearsInformation For questions 3 - 5, solve the given rational equation. Then, fill in the blanks to give the solutions. Write the smaller value first and write fractions in decimal form. If an answer blank is not needed, write NA. Do not insert spaces in answers. Question 3 10 4 5 + Not yet x2 - 2x X x- 2 answered Points out of The solutions are x = and x = 20.00 Question 4 x - 6 x- 7 x+ 111 Not yet x - 4 X - 3 x2-7x+12 answered Points out of The solutions are X = and x = 20.00 Question 5 3x - 3 x-7 x - 2 = Not yet x2 - 13x+ 40 x2-19x+ 70 x2-22x+ 112 answered Points out of The solutions are x = and x = 20.00 E