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- Michael is draining an aquarium. The graph below shows the amount of water (in liters) in the aquarium versus time (in minutes). A. What is the amount of water (per liter) in the aquarium at 0 minutes ? B. Choose the statement that best describes How the time and a water are related. Then give the value requested. (See pictures)(a) The graph of y = f(x) + 7 is obtained from the graph of y = f(x) by shifting (left, right, up, or down ?) 7 units.(b) The graph of y = f(x + 7) is obtained from the graph of y = f(x) by shifting (left, right, up or down ?) 7 units.Recall that revenue is related to price and the number of widgets sold. Assume that the annual widget sales match the annual widget demand, and construct a model for revenue using the model for price that you found in the Price section. Find the model for revenue R ( x ), where R ( x ) is the total annual revenue in dollars for x widgets sold, and write it as R ( x ) = a x 2 + b x + c. Note: You are using the fact that R ( x ) = x ⋅ p ( x ), not creating a table of data. Price of Widgets Annual widget demand x (widgets) Price per widget p ($/widget) 10 147 20 132 30 125 40 128 50 113 60 97 70 85 80 82 90 79 100 53 Enter the value for a. Enter the value for b. Enter the value for c. Use the revenue model R ( x ) = a x 2 + b x + c. Compute R ( 45 ), rounded to the nearest tenth.
- How does the graph of g(x)=4^x+5 compare to the function represented by the table at the right? X|-2,-1,0,1,2 Y|17/16,5/4,2,5,17Consider the function f (x) = a(x-p)(x-q), shown on the following graph. Find the equation of the axis of symmetry. Explain. 2b.Write down the value of p and q Explain your reasoning. 2c. Find the value of a.Scientists are measuring a distant planet's temperature. The graph shows the temperature (in ) versus the height (in kilometers) above the planet's surface. (a) What is the temperature at 0 kilometers? (b) Choose the statement that best describes how the height and temperature are related. Then fill in the blank.
- c. Complete the analysis (be sure to include graphs as appropriate to the test). Show me calculations and results from excel. d. What is the interpretation of your results?Which statement correctly compares the function shown on the graph with the function y=6x - 1? A. The function shown on the graph has a smaller rate of change, but a higher starting point. B. The function shown on the graph has a smaller rate of change and lower starting point. C. The function shown on the graph has a greater rate of change and a higher starting point. D. The function shown on the graph has a greater rate of change and a lower starting point.A box is formed by cutting squares from the four corners of a sheet of paper and folding up the sides. The graph below shows how the volume of the box in cubic inches, V, is related to the length of the side of the square cutout in inches, x. Suppose the largest possible cutout length is 3.5 inches. Over what interval of xx does the volume of the box decrease as the cutout length gets larger? (Enter your answer as an interval.)