Functions and Polynomials

1 Consider the function f(x) = 2x- - 12x - 2. 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) = - 2x2 + 20x - 4. 2 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. Identify the function's domain and its range. 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 40, its height, f(x), in feet, can be modeled by f(x) = - 0.01x-+ 0.8x + 5.4, where x is the shot's 50 horizontal distance, in feet, from its point of release. Use this model to solve parts (a) through (c) and verify your Shot Puts Height 30 answers using the graph. 20 a. What is the maximum height of the shot and how far from its point of release does this occur? b. What is the shot's maximum horizontal distance, to the nearest tenth of a foot, or the distance of the throw? c. From what height was the shot released? 4 A ball is thrown upward and outward from a height of 5 feet. The height of the ball, f(x), in feet, can be modeled by f(x) = - 0.1x + 1.2x +5 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. mong all pairs of numbers whose difference is 4, find a pair whose product is as small as possible. What is the minimum product? Farmer Ed has 150 meters of fencing, and wants to enclose a rectangular plot that borders on a river. If Farmer Ed does not fence the side along the river, find the length and width of the plot that will maximize the area. What is the largest area that can be enclosed? Alex has 400 yards of fencing to enclose a rectangular area. Find the dimensions of the rectangle that maximize the enclosed area. What is the maximum area? A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the 8 playground. Eight hundred and forty feet of fencing is used. Find the dimensions of the playground that maximize the total enclosed area. What is the maximum area? 9 Determine whether the function is a polynomial function. If it is, identify the degree. f(x) = 8x +6x4 Determine whether the function is a polynomial function. If it is, identify the degree. 10 h( x)= 5x3 +4x2 +=