A certain skincare company's profit in millions of dollars, P(t), can be modeled by the polynomial function P(t) = -2t +8t2 + 2t, where t represents the number of skincare items produced, in thousands. Today, the company produces 1 thousand products for a profit of $8 million. According to the graph of the function, what other quantity of product would result in the same profit? What is the inverse of the function f (x) = 3(x + 2)2 - 5, such that x -2? The route that a trolley takes around a city can be represented by the functions x + y = 10. A train track's path can be described by the function x + y = 4. At which location(s) will the trolley and train meet? Given f (x) = x + 3x + 4, what is f(2+h)-f(2) h equal to? Given the following table with selected values of f (x) and g(x), evaluate f (g(1)). X -6-4 1 3 4 f (x) 4 g(x) 1 4 3 -4-6 -1-61 3 The table gives a partial set of values of a polynomial h(x), which has a leading coefficient of 1. 0 12 h(x) 0 -23 -12 00 X -3-2 If every x-intercept of h(x) is shown in the table and has a multiplicity of one, what is the equation of the polynomial function? You find a rare comic book at a yard sale and determine that the price of the comic book, y, measured in hundreds of dollars, after x years can be represented by the following graph. -5-4-3-2 O $6 O $17 O$1,700 24 2822898 O $6,000 23 21 20 19 18 17 16 15 14 13 3210 12 11 10 8 6 5 NT 321 -2 Based on the graph, what is the cost of the rare comic book after 3 years? 1 3 4 6 7 8 9 10 11 12 13 14 15 16 Given f (x) = 2x+1-3, what is f-1(x)? The kinetic energy, k, the amount of energy that a moving object has, can be found for a particular roller 2k coaster by the radical function v = If the velocity, v, of the roller coaster is 20 meters per second, 1,000 what is the kinetic energy?