College Algebra

Consider the function f(x) = 3x - 6x - 5. a. Determine, without graphing, whether the function has a minimum value or a maximum value. b. Find the minimum or maximum value and determine where it occurs. c. Identify the function's domain and its range. Consider the function f(x) = - 2x + 16x - 6. Determine, without graphing, whether the function has a minimum value or a maximum value. Find the minimum or maximum value and determine where it occurs. C. Identify the function's domain and its range. 3 An athlete whose event is the shot put releases a shot. When the shot whose path is shown by the graph to the right is released at an angle of 35, its height, f(x), in feet, can be modeled by f(x) = - 0.01x-+ 0.7x + 6.2, where x is the shot's $50 40 horizontal distance, in feet, from its point of release. Use this model to solve parts (a) through (c) and verify your 30 answers using the graph. 20 3 10 0 20 40 60 80 100 Shot Put's Horizontal Distance A ball is thrown upward and outward from a height of 6 feet. The height of the ball, f(x), in feet, can be modeled by f(x) = - 0.3x +2.1x+6 where x is the ball's horizontal distance, in feet, from where it was thrown. Use this model to solve parts (a) through (c). a. What is the maximum height of the ball and how far from where it was thrown does this occur? b. How far does the ball travel horizontally before hitting the ground? c. Using the answers from above, graph the function that models the ball's parabolic path. 5 Among all pairs of numbers whose difference is 14, find a pair whose product is as small as possible. What is the minimum product? A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. Three hundred and sixty feet of fencing is used. Find the dimensions of the playground that maximize the total enclosed area. What is the maximum area