MATH 107 Quiz

MATH 107 Quiz 4 MATH 107_SU21 QUIZ 4 Name:_ Jonathan Russe____ Date:_7/24/2021_ Please show your work for all problems, and express your answers using exact values. Express fractions in simplest form, including rationalizing all denominators. Write complex numbers in the form π‘Ž + 𝑏𝑖. Problem/Solution 1 score Find all real and non-real solutions. a) (π‘₯ 2 βˆ’ 1)(3π‘₯ βˆ’ 2) = π‘₯(π‘₯ + 1)(π‘₯ βˆ’ 2) βˆ’ 3(π‘₯ βˆ’ 1) b) 2𝑦 2 βˆ’ 2√3𝑦 βˆ’ 3 = 𝑦 2 βˆ’ 5 2 Find all solutions. Write any complex numbers in the form π‘Ž + 𝑏𝑖. 2π‘₯ + 1 = 3 3π‘₯ 2 + 4π‘₯ + 3 π‘₯+2 For the polynomial function 𝑓(π‘₯) = (π‘₯ βˆ’ 1)2 (2π‘₯ + 3) a) State the leading term, leading coefficient, a, and degree, n. b) Describe the end behavior. c) Find the zeros and the multiplicity, m, of each. State whether the graph will cross the x-axis or rebound at each of the zeros. d) For each interval, evaluate the function using a test point. Use your results to create a sign chart. 4 The height a model rocket reaches can be described by the function β„Ž(𝑑) = βˆ’16𝑑 2 + 180𝑑 where t = time in seconds h = height in feet. Page 1 of 3 MATH 107 Quiz 4 a) How long does it take the rocket to reach maximum height? Round time to two decimal places. b) What is its maximum height? Round down to the nearest foot. 5 Continuation of question 4 a) From a nearby viewpoint, onlookers can see the rocket when it is at least 360 ft above the ground. During what times after liftoff is the rocket visible from this viewpoint (round to two decimal places)? b) Based on your result from part c), do you expect the rocket to be visible from the viewpoint 10 seconds after liftoff? Confirm your answer by calculating the rocket’s height for this time. 6 For the rational function 𝑓(π‘₯) = 2π‘₯ 2 βˆ’3π‘₯βˆ’9 π‘₯ 2 βˆ’3π‘₯ a) State the domain using interval notation. b) Write the equation of any vertical asymptotes. c) Identify the coordinates of any holes. 7 Continuation of question 6 a) Write the equation of any horizontal asymptotes. Explain your reasoning. b) Using Desmos, create the graph, showing any holes and showing asymptotes as dashed lines. Include axis labels. 8 Continuation of question 6 – 7 Page 2 of 3 MATH 107 Quiz 4 a) State the behavior of the function as it approaches any vertical asymptotes. b) State the behavior of the function as it approaches any horizontal asymptotes. 9 Given the function𝑓(π‘₯) = inequality π‘₯ 2 βˆ’5π‘₯+4 , use π‘₯+4 the following steps to solve the rational π‘₯ 2 βˆ’ 5π‘₯ + 4 β‰₯0 π‘₯+4 a) Identify the zeros of the function. b) Identify any asymptotes and/or holes. c) For each interval, evaluate the function using a test point. Use your results to create a sign chart. d) State the solution set of the rational inequality using interval notation. 10 Solve the equation and show the check of your work. π‘₯ π‘₯ βˆ’ 1 π‘₯ 2 + 3π‘₯ βˆ’ 1 βˆ’ = π‘₯ + 1 π‘₯ + 2 π‘₯ 2 + 3π‘₯ + 2 Page 3 of 3
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