4 / 11 / 22 1Estefania Hagins Math 200 Problem 8. A baseball is launched into the air with an upward velocity of 106 feet per second. The height of the baseball after t seconds can be represented by the function f (t) given by f(t) = -16t2 + 106t + 9.3. (Round all your answers to three decimal places, if needed.) a) Find the time it takes for the baseball to reach its maximum height. b) What is the maximum height? c) When will the baseball hit the ground? Problem 9. Expand the logarithmic expression log (7+1)3 ) . Show your work. Problem 10. Solve the equation for x: log56 x + log56(x - 1) = 1. Problem 11. Certain radioactive material decays in such a way that the mass remaining after t years is given by the function: m(t) = 320e -0.025t, where m(t) is measured in grams. (Round your answers to one decimal place, if needed.) a) Find the mass of the material at time t = 0. b) How much of the mass remains after 50 years? c) How long will it take for the sample to lose half of its mass? Problem 12. Determine the amplitude and period of the function y = 3 cos ( x ). Then, graph the function over its single period using five key points. Problem 13. Find all solutions of the equation 2 cos x - 2 sin x cos x = 0 on the interval [0, 27). Give the exact values only. Problem 14. a) Let t be a real number and let P , - 2 ) be the point on the unit circle that corresponds to t. Find the values of cost and tan t, and then evaluate 2 cost + tan't. b) Find the exact value of sin-1 (sin ()) Problem 15. Solve the triangle ABC, if b = 121, c = 160, LB = 40. Assume ZA is opposite to side a, LB is opposite to side b, and LC is opposite to side c.Problem 1. If f (x) has an inverse function f-1(x), could either the graph of f (x) or the graph of f-1(x) be symmetric with respect to the y-axis? Explain your reasoning or use an example to illustrate your answer. Problem 2. Let f (x) = In ( + 9) and g(x) = _, . Find the domain of (fog) (x). Write your answer in interval notation. following: Problem 3. For the function f (x) = 6x2 - x - 2 , evaluate and fully simplify each of the a) f ( x + h ) = f(ath ) - f(xx ). h Instructions: Simplify answers as much as possible. Expressions such as 3(x+5) and (x + h)2 should be expanded. Also, combine like terms, so 7x+3x should be written as 10x. Problem 4. a) Find the vertex, axis of symmetry, and intercepts, if any, of the function f (x) = -x2 - 6x - 10. b) Use this information to graph the function. Label key points on the graph. c) State the domain and range of f(x). d) Find the intervals where the function is increasing/decreasing. e) Does f(x) have local maxima/minima? If so, find those local maxima/minima and indicate the values of x where they attained. Problem 5. Find the standard form of the equation of the circle x2 + y2 - 2x + 12y + 12 = 0. Then, state the center and radius of the circle. Problem 6. Sketch a graph of -2x - 7, if x 5 -4, f ( x ) = 1 , if - 4 1. What is the domain of f (x)? What is the range of f (x)? Problem 7. a) Describe the transformation(s) that can be applied to the function g(x) = ex to obtain the graph of f (x) = e-*+7. b) State the domain and range of f(x). c) Sketch the graph of f(x)