1) A parabola opening d
AP CALCULUS AB Summer Review Packet Find the equation for the function described for questions 1 – 4: 1) A parabola opening downward with its vertex at (2, 5) 2) A parabola with x intercepts of -2 and 1, and with a y intercept of 3. 3) A line parallel to 3x – 2y = 10 that goes through the point (-1, 4) ax 4) A rational function in the form f (x) = with a vertical asymptote at x = 2 and a x+b horizontal asymptote of y = – 5. 5) The entire function of the graph of f (x) is shown below. Answer the following questions.
(a) What is the domain of f (x)? (b) What is the range of f (x)? (c) List all the zeros of f (x). (d) List all intervals on which f (x) is increasing. (e) Is f (x) concave up or concave down at x = 6? (f) What is f (4)? (g) Is f (x) invertible? Explain why or why not. For questions 6 – 17, write an equation for the graph shown. 6) 7)
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For questions 18 – 21, solve the inequality. Write the solution in interval notation. 18) x 2 − 16 < 0 19) x 2 + 6x − 16 ≤ 0 20) x 2 − 3x ≥ 10 21) (x − 1)(x + 2)2 (x − 3) > 0 22) A flight from Dulles Airport in Washington, DC, to LaGuardia Airport in New York City has to circle LaGuardia several times before being allowed to land. Plot a graph of the distance of the plane from Washington, DC, against time, from the moment of takeoff until landing. 23) The graph of f (x) opens upward and the graph of g (x) is a line with a negative slope. Describe the graph of g (f (x)) in words. 24) What is the doubling time of prices, which are increasing by 5% per year? 25) The air in a factory is being filtered so that the quantity of a pollutant, P (in mg/liter), which is decreasing according to the function P = P0 e− kt , where t is in hours. If 10% of the pollution is removed in the first 5 hours, answer the following questions: (a) What percentage of the pollution is left after 10 hours? (b) How ling is it before the pollution is reduced by 50%? (c) Plot a graph of pollution against time. Show the results of your calculations to (a) and (b) on your graph. (d) Explain why the quantity of pollutant might decrease this way. 26) In an electrical outlet, the voltage V in volts is given as a function of time, t in seconds by the formula V = V0 sin(120π t) . (a) What does V0 represent in terms of voltage? (b) What is the period of this function? (c) How many oscillations are completed in 1 second?
27) Match the following graphs to the functions. 0 < b < a
(a) What is the domain of f (x)? (b) What is the range of f (x)? (c) List all the zeros of f (x). (d) List all intervals on which f (x) is increasing. (e) Is f (x) concave up or concave down at x = 6? (f) What is f (4)? (g) Is f (x) invertible? Explain why or why not. For questions 6 – 17, write an equation for the graph shown. 6) 7)
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For questions 18 – 21, solve the inequality. Write the solution in interval notation. 18) x 2 − 16 < 0 19) x 2 + 6x − 16 ≤ 0 20) x 2 − 3x ≥ 10 21) (x − 1)(x + 2)2 (x − 3) > 0 22) A flight from Dulles Airport in Washington, DC, to LaGuardia Airport in New York City has to circle LaGuardia several times before being allowed to land. Plot a graph of the distance of the plane from Washington, DC, against time, from the moment of takeoff until landing. 23) The graph of f (x) opens upward and the graph of g (x) is a line with a negative slope. Describe the graph of g (f (x)) in words. 24) What is the doubling time of prices, which are increasing by 5% per year? 25) The air in a factory is being filtered so that the quantity of a pollutant, P (in mg/liter), which is decreasing according to the function P = P0 e− kt , where t is in hours. If 10% of the pollution is removed in the first 5 hours, answer the following questions: (a) What percentage of the pollution is left after 10 hours? (b) How ling is it before the pollution is reduced by 50%? (c) Plot a graph of pollution against time. Show the results of your calculations to (a) and (b) on your graph. (d) Explain why the quantity of pollutant might decrease this way. 26) In an electrical outlet, the voltage V in volts is given as a function of time, t in seconds by the formula V = V0 sin(120π t) . (a) What does V0 represent in terms of voltage? (b) What is the period of this function? (c) How many oscillations are completed in 1 second?
27) Match the following graphs to the functions. 0 < b < a
