Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Functional decomposition wikipedia , lookup
Big O notation wikipedia , lookup
Non-standard calculus wikipedia , lookup
Dirac delta function wikipedia , lookup
Mathematics of radio engineering wikipedia , lookup
Continuous function wikipedia , lookup
Principia Mathematica wikipedia , lookup
Function (mathematics) wikipedia , lookup
PC Sec. 1.2-1.4 Study Guide Haggenmaker Fall 2013-2014 Short Answer 1. A lake’s fish population over eight years is modeled by p(x) = 1.96x3 – 30x2 + 196x + 244. Use the function to estimate p(2) and p(6), the populations in the second and sixth years. 2. Find f (a + 1) for f (x) = 2(x – 1)2 + 3x. 3. What is the domain and range of the function shown in the graph? 4. Find the average rate of change of f (x) = 2.5x2 – 7x + 5 on the interval [2, 5]. 5. Evaluate f (–2) if f (x) = 3x2 – 2x. 6. Use the graph of f to find the domain and range of the function. 7. Graph f(x) = x3 – 4x using a graphing calculator. Determine whether the function is even, odd, or neither. If even or odd, describe the symmetry of the graph. Determine whether the function is continuous or discontinuous at the given x-value. 8. 9. 10. Use the graph of f (x) to describe its end behavior. 11. Find the average rate of change of f (x) on the interval [–3, –1]. Use the graph to determine the domain and range of the relation. y 12. x y 13. x 14. y 1 –4 4 x –1 15. Find for . 16. Use the graph of f(x) to estimate f(3). y 10 8 6 4 2 –10 –8 –6 –4 –2 –2 –4 –6 –8 –10 2 4 6 8 10 x 17. Identify the y-intercept and zeros of . 18. Use the graph below to identify the domain and range. y 10 8 6 4 2 –10 –8 –6 –4 –2 –2 2 4 6 8 10 x –4 –6 –8 –10 19. Given the point determine the points that are symmetric to this point with respect to the x-axis, the y-axis, and the origin respectively. 20. The graph below is a portion of a complete graph. Sketch the complete graph assuming it is symmetric with respect to the x-axis. y 10 –10 10 x –10 21. Is the following function an even function, an odd function, or neither? 22. Determine between which consecutive integers the real zeros of [-10, 10]. are located on the interval 23. Determine between which consecutive integers the real zeros of interval [-10, 10]. are located on the Without graphing, describe the end behavior of the graph of the function. 24. 25. 26. Graph the function. Determine the interval(s) for which the function is increasing and the interval(s) for which the function is decreasing. 27. 28. 29. Find the relative minimum and the relative maximum points for the graph of 30. Estimate to the nearest 0.5 unit and classify the extrema for the graph of f(x). y 32 28 24 20 16 12 8 4 –5 –4 –3 –2 –1 –4 –8 –12 –16 –20 –24 –28 –32 1 2 3 4 5 x 31. Estimate to the nearest 0.5 unit and classify the extrema for the graph of f(x). y 70 60 50 40 30 20 10 –5 –4 –3 –2 –1 –10 1 2 3 4 5 x –20 –30 –40 –50 –60 –70 32. Find the average rate of change of on [5, 10]. Round your answer to the nearest hundredth. Estimate and classify the critical points for the graph of each function. 33. y 2 1 –2 –1 1 –1 –2 2 x PC Sec. 1.2-1.4 Study Guide Answer Section Haggenmaker SHORT ANSWER 1. ANS: 532; 763 2. ANS: 2a2 + 3a + 3 3. ANS: ; 4. ANS: 10.5 5. ANS: 16 6. ANS: 7. ANS: odd; symmetric about origin 8. ANS: discontinuous; jump 9. ANS: discontinuous; infinite 10. ANS: 11. ANS: –43 12. ANS: Domain: ; Range: ; No, it fails the vertical line test. OBJ: 1-1.2 Identify and evaluate functions and state their domains. NAT: 2 TOP: Functions 13. ANS: Domain: all positive real numbers, including zero; Range: all real numbers; No, it fails the vertical line test. OBJ: 1-1.2 Identify and evaluate functions and state their domains. NAT: 2 TOP: Functions 14. ANS: Domain: all real numbers; Range: ; Yes, for any value of x there is only one value of y. OBJ: 1-1.2 Identify and evaluate functions and state their domains. Fall 2013-2014 NAT: 2 15. ANS: TOP: Functions = OBJ: 1-1.2 Identify and evaluate functions and state their domains. NAT: 2 TOP: Functions 16. ANS: f(3) = 3 OBJ: 1-2.1 Use graphs of functions to estimate function values and find domains, ranges, y-intercepts, and zeros of functions. NAT: 2 STA: 9-12.P.4 TOP: Analyzing Graphs of Functions and Relations 17. ANS: y-intercept: –12 zeros: 1, –1 OBJ: 1-2.1 Use graphs of functions to estimate function values and find domains, ranges, y-intercepts, and zeros of functions. NAT: 2 STA: 9-12.P.4 TOP: Analyzing Graphs of Functions and Relations 18. ANS: D: [-6, 6), [7, ) R: [-3, ) OBJ: 1-2.1 Use graphs of functions to estimate function values and find domains, ranges, y-intercepts, and zeros of functions. NAT: 2 STA: 9-12.P.4 TOP: Analyzing Graphs of Functions and Relations 19. ANS: OBJ: 1-2.2 Explore symmetries of graphs, and identify even and odd functions. NAT: 2 STA: 9-12.P.4 TOP: Analyzing Graphs of Functions and Relations 20. ANS: y 10 –10 10 x –10 OBJ: 1-2.2 Explore symmetries of graphs, and identify even and odd functions. NAT: 2 STA: 9-12.P.4 TOP: Analyzing Graphs of Functions and Relations 21. ANS: odd function OBJ: 1-2.2 Explore symmetries of graphs, and identify even and odd functions. NAT: 2 STA: 9-12.P.4 TOP: Analyzing Graphs of Functions and Relations 22. ANS: -1; 1; OBJ: 1-3.1 Use limits to determine the continuity of a function, and apply the Intermediate Value Theorem to continuous functions. NAT: 2 STA: 9-12.P.10 TOP: Continuity, End Behavior, and Limits 23. ANS: OBJ: 1-3.1 Use limits to determine the continuity of a function, and apply the Intermediate Value Theorem to continuous functions. NAT: 2 STA: 9-12.P.10 TOP: Continuity, End Behavior, and Limits 24. ANS: As x g(x) As x g(x) OBJ: 1-3.2 Use limits to describe end behavior in functions. NAT: 2 STA: 9-12.P.4 | 9-12.P.10 TOP: Continuity, End Behavior, and Limits 25. ANS: As x f (x) As x f (x) OBJ: 1-3.2 Use limits to describe end behavior in functions. NAT: 2 STA: 9-12.P.4 | 9-12.P.10 TOP: Continuity, End Behavior, and Limits 26. ANS: As x h(x) As x h(x) OBJ: 1-3.2 Use limits to describe end behavior in functions. NAT: 2 STA: 9-12.P.4 | 9-12.P.10 TOP: Continuity, End Behavior, and Limits 27. ANS: y 30 20 10 –30 –20 –10 10 20 30 x –10 –20 –30 increasing for and ; decreasing for and OBJ: 1-4.1 Determine intervals on which functions are increasing, constant, or decreasing, and determine maxima and minima of functions. NAT: 2 STA: 9-12.P.4 TOP: Determine whether a function is increasing or decreasing on an interval. 28. ANS: y 10 –10 10 x –10 increasing for decreasing for OBJ: 1-4.1 Determine intervals on which functions are increasing, constant, or decreasing, and determine maxima and minima of functions. NAT: 2 STA: 9-12.P.4 TOP: Determine whether a function is increasing or decreasing on an interval. 29. ANS: is a relative maximum; is a relative minimum OBJ: 1-4.1 Determine intervals on which functions are increasing, constant, or decreasing, and determine maxima and minima of functions. NAT: 2 STA: 9-12.P.4 TOP: Extrema and Average Rates of Change 30. ANS: OBJ: 1-4.1 Determine intervals on which functions are increasing, constant, or decreasing, and determine maxima and minima of functions. NAT: 2 STA: 9-12.P.4 TOP: Extrema and Average Rates of Change 31. ANS: OBJ: 1-4.1 Determine intervals on which functions are increasing, constant, or decreasing, and determine maxima and minima of functions. NAT: 2 STA: 9-12.P.4 TOP: Extrema and Average Rates of Change 32. ANS: 0.08 OBJ: 1-4.2 Determine the average rate of change of a function. NAT: 2 STA: 9-12.P.4 TOP: Extrema and Average Rates of Change 33. ANS: (-0.6, 0.6), maximum; (0.4, -0.2), minimum; (1, 0), maximum; no points of inflection that are critical points OBJ: 1-4.3 Visually locate critical points on the graphs of polynomial functions and determine if each critical point is a minimum, a maximum, or point of inflection. TOP: Extrema and Average Rates of Change