Please answer all questions correctly. I dont need the full work but i do need you to MAKE SURE that you have the correct answer for all of the questions. That being said, I will only give you a perfect rating ONLY if you answer all questions + provide the correct (answers)! IT DOES LOOK LONG BUT I PROMISE THAT IS NOT THAT LONG OR HARD, SO PLEASE DONT GET DISCOURAGED.

\fThe cost in dollars of making x items is given by the function C(x) = 20x + 500. a. The fixed cost is determined when zero items are produced. Find the fixed cost for this item. $ 500 b. What is the cost of making 20 items? $ 900 c. Suppose the maximum cost allowed is $2500. What are the domain and range of the cost function, C(a)? Domain: [-00, 100) Preview Range: (-00,2500) PreviewFind the average rate of change on the interval specified for real numbers b (where b * 0). g(x) = 4x2 - 2 on [0, b] PreviewFind the average rate of change on the interval specified for real numbers b. g(x) = 2x - 2 on [ - 5, - 5 + b] PreviewFind the average rate of change on the interval specified for real numbers h. 1 g(x) = x - 2 on - 3, - 3 + h] PreviewFor the following exercise, find the average rate of change of the function on the interval specified. f(a) = x2 on [2, 3]For the following exercise, find the average rate of change of the function on the interval specified. f(x) = 4 - 2x2 on [ - 3, - 1]\fFor the following exercise, find the average rate of change of the function on the interval specified. (t2 - 3) (t + 1) p(t) = on [1, 3] t2 + 2 PreviewLet f(a) = -. Find the number c such that the average rate of change of the function f on the interval (1, c) is C =The following is the graph of the function f. 7 Use the graph to nd the intervals on which the function is increasing or decreasing. Increasing: Preview Decreasing: Preview The following is the graph of the function f. 48 44 40 36 32 28 24 20 16 -3 -2 -1 do - 12 -16 -20- -24 -28 -32 -36 -40 44 48 Estimate the intervals where f is increasing or decreasing. Increasing: Preview Decreasing: Preview Estimate the point at which the graph of f has a local maximum or a local minimum. Local maximum: ( Local minimum: (The table below gives the annual sales (in millions of dollars) of a product from 1998 to 2006. Year Sales in millions of dollars E 196 E 213 % 227 R 238 E 243 E 246 M 243 E 238 % 227 What was the average rate of change of annual sales between 2001 and 2003? What was the average rate of change of annual sales between 2001 and 2005? At the start of a trip, the odometer on a car read 22435. At the end of the trip, 12.5 hours later, the odometer read 23085. Assuming the scale on the odometer is in miles, what is the average speed the car traveled during the trip? Round to the nearest tenth of a mile. miles per hour Near the surface of a planet far away, the distance an object falls is a function of time. It is given by d(t) = 3.6667t2, where t is in seconds and d(t) is in feet. If an object is dropped from a certain height, nd the average velocity of the object from t = 1 to t = 4. Round to the nearest hundredth of a foot. feet per second For the following exercises, determine the domain for each function in interval notation. Given f(x) = x2 + 6x and g(x) = 5 - x2, find f + g, f - g and - ( f + g) (20) = Preview Domain: Preview (f - g) (20) = Preview Domain: Preview (!) (2) = Preview Domain: PreviewFor the following exercise, use each pair of functions to find f(g(x)) and g(f(x)). Simplify your answers. f(a) = 22 + 4, g(20) = Vac+1 f(g(x)) = Preview g(f (2)) = PreviewFor the following exercise, use each pair of functions to find f(g(x) ) and g(f(x)). Simplify your answers. 1 f (a) = x - 2 ' 9 (20) = + 2 f(g(a)) = Preview 9(f (20) ) : PreviewFor the following exercise, use each set of functions to find f(g(h(x))). f(a) = 24+ 6, g(20) = 2+5, h(a) = vac PreviewFor the following exercises, find functions f(x) and g(x) so the given functions can be expressed as h(x) = f(g(x)). There are multiple possible answers. If the answers require exponents, enter the answer with an exponent in f(x) but not in g(x). 5 ha) = (2 + 5) 2 f (2) = Preview g(2) = PreviewFor the following exercises, nd functions f(:::) and 9(3) so the given functions can be expressed as 11(3) = f(9(9r))- has) = m \"95) = Preview m = \fFor the following exercise, find the domain and range of the function below using interval notation. 10 10 -9 -8 -7 -6 -5 -4 -3 -2 1 1 2 3 4 5 6 7 8 9 16 Domain: (-3,5] Preview Range: [-6,1] Preview