Indicate whether the statement is true or false. _________ The…

Question Answered step-by-step Indicate whether the statement is true or false. _________ The… Indicate whether the statement is true or false._________ The reciprocal of every linear function has a vertical asymptote.__________An even function is symmetrical about the origin.__________ ??(??) = 1/(x-5)2 is always positive. ??__________ All polynomial functions that are members of the same family will have the same x-intercepts.__________ ??(??) ? +? as ?? ? 2?? for the function ??(??) = 1/3x-6 ? ???????? Multiple Choice (1 mark each)Identify the choice that best completes the statement or answers the question.6. Which of the reciprocal functions has a vertical asymptote at ?? = 5/2???? ?a. ??(??)= 1/(x+5/2) ????????c. ??(??)= 1/x+2?? ????????b. ??(??)= 1/2x+5?? ??????d. ??(??)= 1/2x-5 ????????7. Which of the following has a horizontal asymptote at y = 0 ?a. ??(??)= 1/3-x?? ??????b.??(??)= -1/x+2 c. ??(??)= 1/17x+4d.??(??)= all of the above??????????8. What is the x-intercept of ??(??) = 1/3x-4 ?? ? ????????a. ??(??)= -1/4b. ??(??)= 1/4c. ??(??)= 4/3?? ??????d. There are no x-intercepts 9. Over what interval(s) is the graph of the rational function decreasing?a. x<-2,-24 c. x>4d. x<-2, -2 -2x+9  a.b. c. d.  Short Answer11. Based on the function f(x) 2x-4/x+4, fill in the following table of characteristics and graph the function. ??????Use the space below to show your work. Be sure that your steps/work is easy to find and organized. (15 marks) x-intercept(s)y-interceptdomainrangevertical asymptote(s)horizontal asymptotepositive intervalnegative intervalintervals of increaseintervals of decrease 12. Using algebraic methods, determine whether the following functions are odd, even, or neither. Be sure to show your work. (4 marks)a) f(x) = x2/(x-2)3 ???? b) f(x) = x2/x2+1 ?? ???????? Applications13. Describe how the graph of ?? = ?2??[3(?? ? 1)] ? 4 can be obtained from the graph of ??(??) = ??^4??. Be sure to use full sentences when describing the transformations. (4 marks) 14. The population of a small town is modelled by the function P(t) = 20(4t+3)/2t+5, where P(t) is the ????????population, in thousands, and t is time, in years, since the start of 1990. a)  Is the population currently increasing or decreasing? Justify your answer. (2 marks)b)  The town will need its own transit system if the population exceeds 50 000. Will the town’s population ever exceed 50 000? Explain. (2 marks)15. Polluted water from a factory flows into a pond. The concentration of pollutant, c, in the pond at time t minutes is modelled by the equation c(t) = 8 – 8000 (1/1000+2t), where c is measured in kg/m3. When will the concentration of pollutants in the pond reach 6 kg/m3? (4 marks) Thinking16. Solve 2x-1/x-5 > x+1/x+5. (5 marks) ?????? ??????17. The following set of points belong to a specific function: {(-3,0)(-2,4), (-1,0 ), (0,-6),(1,-8), (2,0),(3,24)} Based on the set of points answer the following questions:a) What type of function does the set of points produce? Justify your answer. (2 marks)b) Write an equation for this function based on the set of points that have been given. (3 marks Math MATH MHF4UO Share QuestionEmailCopy link Comments (0)