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- Graph f(x)=2x10. Picka set of5 ordered pairs using inputs x=2,1,5,6,9 and use linear regression to verify the function.. Graph the function f (x) = 2x3 - 3x2 - 6x on thewindows given in parts (a) and (b). Which windowgives a complete graph?a. [ -5, 5] by [ -5, 5]b. [ -10, 10] by [ -10, 10]suppose the profit of producing (and selling) x bottlesof soda is given by the function. P(x) = −x2 + 60x − 500, x ≥ 0 Answer the following questions and provide explanations. Writeshort verbal explanations (with some graphs) targeted to audienceswho have never taken a precalculus class.(a) At least how many bottles should be produced (and sold) inorder to have some profit?(b) How many bottles should be produced in order to maximizethe profit? Assume you sell all that are produced.
- A market analyst working for a small-appliance manufacturer finds that if the firm produces and sells x blenders annually, the total profit (in dollars) is P(x) = 8x + 0.3x2 − 0.0013x3 − 374. Graph the function P in an appropriate viewing rectangle and use the graph to answer the following questions. (a) When just a few blenders are manufactured, the firm loses money (profit is negative). (For example, P(10) = −265.30, so the firm loses $265.30 if it produces and sells only 10 blenders.) How many blenders must the firm produce to break even? (Round your answer to the integer that gives the company the least positive profit.)(b) Does profit increase indefinitely as more blenders are produced and sold? Yes No If not, what is the largest possible profit the firm could have? (Round your answer to the nearest cent. If an answer does not exist, enter DNE.)$For the function y=x2+x+2, which statements are true? Select all that apply. a. The graph of the function opens upward, so it has a minimum of y=7/4 at x=-1/2 b. The equation written in vertex form is y=(x+1/2)2 + 7/4 c. The graph of the function opens downward. so it has a maximum of y= 7/4 at x= -1/2 d. The equation written in vertex form is y=(x+1/2)2Dharma graphed the parents function f(x)=x and h(x) on the same grid. If h(x) is steeper than the parents function and shifted to the right, which of the following could represent h(x)? 1. H(x)=3f(x-5) 2. None of these 3. H(x)= -f(x) 4. H(x)=0.5(x-2) 5. H(x)=2f(x)+6
- a. Complete the table of values for the functiony = x3, plot the values of x and y as points ina coordinate plane, and draw a smooth curvethrough the points. b. Graph the function y = x3with a graphing calculator, using the viewing window xmin = -4,xmax = 4, ymin = -30, ymax = 30.c. Compare the graphs in parts (a) and (b).A graphing calculator is recommended. A market analyst working for a small-appliance manufacturer finds that if the firm produces and sells x blenders annually, the total profit (in dollars) isP(x) = 8x + 0.3x2 − 0.0013x3 − 376.Graph the function P in an appropriate viewing rectangle and use the graph to answer the following questions. (a) When just a few blenders are manufactured, the firm loses money (profit is negative). (For example, P(10) = −267.30, so the firm loses $267.30 if it produces and sells only 10 blenders.) How many blenders must the firm produce to break even? (Round your answer to the integer that gives the company the least positive profit.) (b) Does profit increase indefinitely as more blenders are produced and sold?YesNo If not, what is the largest possible profit the firm could have? (Round your answer to the nearest cent. If an answer does not exist, enter DNE.)10. Jingle Bells Inc. has received a rush order for as many of two types of Easter eggs as can be purchased and shipped during a 2-week period. Preliminary analysis by Jingle Bells indicates that the profit on this order isrelated to the number of each type of Easter egg manufactured by the function:P(x1 , x2) = – x12– x22 + 12x1 + 10x2 + 61where x1 = thousands of units of Type 1 eggs and x2 = thousands of units of Type 2 eggs. Because of other commitments over the two weeks, Jingle Bells has available only 60 hours in the Shipping and Packaging Department to get the order out the door. It is estimated that every 1000 units of Type 1 eggs will require 20 hours in the department and every 1000 units of Type 2 eggs will require 30 hours.i) Formulate a mathematical model that can be used to determine how many thousands of each Type of egg should be manufactured in the two-week period so as to maximise profit.ii) Find a solution to your mathematical model.
- In Exercises use graphing software to determine which of thegiven viewing windows displays the most appropriate graph of thespecified function.ƒ(x) = 5 + 12x - x3a. [-1, 1] by [-1, 1] b. [-5, 5] by [-10, 10]c. [-4, 4] by [-20, 20] d. [-4, 5] by [-15, 25]If k(x) = a(x) x b(x) then what is the graph of k(x)?use graphing software to determine which of the given viewing windows displays the most appropriate graph of the specified function. 1. ƒ(x) = x3 - 4x2 - 4x + 16 a. [-1, 1] by [-5, 5] b. [-3, 3] by [-10, 10] c. [-20, 20] by [-100, 100] d. [-5, 5] by [-10, 20].