{"answerArea": {"calculator": false, "chi2Table": false, "periodicTable": false, "tTable": false, "zTable": false}, "hints": [{"content": "The $y$-intercept is the point of intersection between the graph of the function $C(S)$ and the $y$-axis, which is the point on the graph where $S=0$. \n\nThe $y$-intercept in this graph is $(0,0)$, which means that *when the car doesn't move, it doesn't consume any fuel.*\n\n\n[[☃ image 1]]\n\n", "images": {}, "replace": false, "widgets": {"image 1": {"alignment": "block", "graded": true, "options": {"alt": "The first quadrant of a coordinate plane. The x-axis scales by ten and is labeled S for the car's speed in kilometers per hour. The y-axis scales by two and is labeled C of S for the fuel efficiency of the car. The graph of the function is a continuous curve. From left to right, it starts at zero, zero and increases through the point ten, seven, the point twenty, thirteen, and the point forty, nineteen until it reaches a local maximum at fifty-five, twenty. Then it decreases through the point seventy, nineteen, the point ninety, sixteen, and the point one hundred twenty, twelve. All values are estimates. The point zero, zero is plotted on the function.", "backgroundImage": {"height": 231, "url": "web+graphie:${☣ LOCALPATH}/images/1bc43e00a3d2fc81b651268e0e5a38f4d2bb9167", "width": 231}, "box": [231, 231], "caption": "", "labels": [], "range": [[0, 10], [0, 10]], "static": false, "title": ""}, "static": false, "type": "image", "version": {"major": 0, "minor": 0}}}}, {"content": "A relative maximum (or minimum) point is a point that is higher (or lower) than all of the points surrounding it.\n\nThis graph has a relative maximum point where $C(S)=20$, which means that *the most efficient the car can get is $\\textit{20 km/l}$.*\n\n\n\n[[☃ image 1]]\n\n", "images": {}, "replace": false, "widgets": {"image 1": {"alignment": "block", "graded": true, "options": {"alt": "The first quadrant of a coordinate plane. The x-axis scales by ten and is labeled S for the car's speed in kilometers per hour. The y-axis scales by two and is labeled C of S for the fuel efficiency of the car. The graph of the function is a continuous curve. From left to right, it starts at zero, zero and increases through the point ten, seven, the point twenty, thirteen, and the point forty, nineteen until it reaches a local maximum at fifty-five, twenty. Then it decreases through the point seventy, nineteen, the point ninety, sixteen, and the point one hundred twenty, twelve. All values are estimates. The point fifty-five, twenty is plotted on the function.", "backgroundImage": {"height": 231, "url": "web+graphie:${☣ LOCALPATH}/images/eb0e2051699f343685c499904aab171c0df3febd", "width": 231}, "box": [231, 231], "caption": "", "labels": [], "range": [[0, 10], [0, 10]], "static": false, "title": ""}, "static": false, "type": "image", "version": {"major": 0, "minor": 0}}}}, {"content": "An increasing (or decreasing) interval is a domain interval over which the function values increase (or decrease) as the input variable increases.\n\nIn this graph, the interval $[0,55]$ is an increasing interval. This means that *as the car accelerates towards about $\\textit{55 km/h}$, it gets more efficient.*\n\n\n\n[[☃ image 1]]\n\n", "images": {}, "replace": false, "widgets": {"image 1": {"alignment": "block", "graded": true, "options": {"alt": "The first quadrant of a coordinate plane. The x-axis scales by ten and is labeled S for the car's speed in kilometers per hour. The y-axis scales by two and is labeled C of S for the fuel efficiency of the car. The graph of the function is a continuous curve. From left to right, it starts at zero, zero and increases through the point ten, seven, the point twenty, thirteen, and the point forty, nineteen until it reaches a local maximum at fifty-five, twenty. Then it decreases through the point seventy, nineteen, the point ninety, sixteen, and the point one hundred twenty, twelve. All values are estimates. The function is highlighted from x equals zero to z equals fifty-five.", "backgroundImage": {"height": 231, "url": "web+graphie:${☣ LOCALPATH}/images/4359da28e64a00f2e9969ebb1ace4b59268e4d80", "width": 231}, "box": [231, 231], "caption": "", "labels": [], "range": [[0, 10], [0, 10]], "static": false, "title": ""}, "static": false, "type": "image", "version": {"major": 0, "minor": 0}}}}, {"content": "To sum it up, the table should look as follows:\n\nFeature | Statement\n:-: | :-:\n$y$-intercept | When the car doesn't move, it doesn't consume any fuel.\nRelative maximum or minimum | The most efficient the car can get is $20\\text{ km/l}$.\nIncreasing or decreasing interval | As the car accelerates towards about $55\\text{ km/h}$, it gets more efficient.", "images": {}, "replace": false, "widgets": {}}], "itemDataVersion": {"major": 0, "minor": 1}, "question": {"content": "A car's fuel efficiency is measured by the distance it can drive per a single unit of fuel. A common unit for efficiency is $\\text{km/l}$, kilometers per liter of fuel.\n\n$C(S)$ models the fuel efficiency of a certain car as a function of the car's speed $S$ (in kilometers per hour).\n\n**Match each statement with the feature of the graph that most closely corresponds to it.**\n\n\n\n[[☃ image 1]]\n\n[[☃ matcher 1]]", "images": {}, "widgets": {"image 1": {"alignment": "block", "graded": true, "options": {"alt": "The first quadrant of a coordinate plane. The x-axis scales by five and is labeled S for the car's speed in kilometers per hour. The y-axis scales by one and is labeled C of S for the fuel efficiency of the car. The graph of the function is a continuous curve. From left to right, it starts at zero, zero and increases through the point ten, seven, the point twenty, thirteen, and the point forty, nineteen until it reaches a local maximum at fifty-five, twenty. Then it decreases through the point seventy, nineteen, the point ninety, sixteen, and the point one hundred twenty, twelve. All values are estimates.", "backgroundImage": {"height": 464, "url": "web+graphie:${☣ LOCALPATH}/images/83cb64bafba92e716ac911ba4c3533cf9665f487", "width": 464}, "box": [464, 464], "caption": "", "labels": [], "range": [[0, 10], [0, 10]], "static": false, "title": ""}, "static": false, "type": "image", "version": {"major": 0, "minor": 0}}, "matcher 1": {"alignment": "default", "graded": true, "options": {"labels": ["**Feature**", "**Statement**"], "left": ["$y$-intercept", "Relative maximum or minimum", "Increasing or decreasing interval"], "orderMatters": false, "padding": true, "right": ["When the car doesn't move, it doesn't consume any fuel.", "The most efficient the car can get is $20\\text{ km/l}$.", "As the car accelerates towards about $55\\text{ km/h}$, it gets more efficient."]}, "static": false, "type": "matcher", "version": {"major": 0, "minor": 0}}}}}