{"answerArea": {"calculator": false, "chi2Table": false, "periodicTable": false, "tTable": false, "zTable": false}, "hints": [{"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 minimum point where $T(d)=-4$, which means that *the coldest temperature outside the car was $\\textit{-4}^\\circ\\textit{C}$.*\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 twenty and is labeled d for the distance drove in kilometers. The y-axis scales by two and is labeled T of d for the temperature, in degrees Celsius, outside the car. The graph of the function is a continuous curve. From left to right, it starts at the y-intercept zero, six and increases through the point ten, nine, the point twenty, eleven point five, and the point thirty, thirteen until it reaches a local maximum at fifty, sixteen. Then it decreases through the point sixty, fifteen point five, the point seventy, fourteen, the point eighty, fourteen, and the point one hundred, five. It continues decreasing through the x-intercept one hundred ten, zero, the point one hundred twenty, negative one, and the point one hundred forty, negative three point five until a local minimum at one hundred fifty, negative four. Then it increases though the point one hundred sixty, negative three point five and the x-intercept one hundred seventy, zero until it reaches a local maximum at one hundred seventy-eight, three point five. Then is decreases to one hundred eighty-five, three, and increases again to two hundred, six. The point one hundred fifty, negative four is plotted on the function.", "backgroundImage": {"height": 214, "url": "web+graphie:${☣ LOCALPATH}/images/892ac97230ce8e61452ad52aa78f5f7e9ec5aadc", "width": 231}, "box": [231, 214], "caption": "", "labels": [], "range": [[0, 10], [0, 10]], "static": false, "title": ""}, "static": false, "type": "image", "version": {"major": 0, "minor": 0}}}}, {"content": "A positive (or negative) interval is a domain interval over which the function values are all positive (or negative).\n\nSince $T(d)<0$ over the interval $[110,170]$, this is a negative interval. This means that *between the $\\textit{110}^\\textit{th}$ and the $\\textit{170}^\\textit{th}$ kilometers, the outside temperature was below zero.*\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 twenty and is labeled d for the distance drove in kilometers. The y-axis scales by two and is labeled T of d for the temperature, in degrees Celsius, outside the car. The graph of the function is a continuous curve. From left to right, it starts at the y-intercept zero, six and increases through the point ten, nine, the point twenty, eleven point five, and the point thirty, thirteen until it reaches a local maximum at fifty, sixteen. Then it decreases through the point sixty, fifteen point five, the point seventy, fourteen, the point eighty, fourteen, and the point one hundred, five. It continues decreasing through the x-intercept one hundred ten, zero, the point one hundred twenty, negative one, and the point one hundred forty, negative three point five until a local minimum at one hundred fifty, negative four. Then it increases though the point one hundred sixty, negative three point five and the x-intercept one hundred seventy, zero until it reaches a local maximum at one hundred seventy-eight, three point five. The function is highlighted from x equals one hundred ten to x equals one hundred seventy.", "backgroundImage": {"height": 214, "url": "web+graphie:${☣ LOCALPATH}/images/207190c2f94aeda592253087d9a5d6eb87b20688", "width": 231}, "box": [231, 214], "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 $[0,50]$ is an increasing interval. This means that *over the first $\\textit{50}\\textit{ km}$, the temperature outside the car got warmer.*\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 twenty and is labeled d for the distance drove in kilometers. The y-axis scales by two and is labeled T of d for the temperature, in degrees Celsius, outside the car. The graph of the function is a continuous curve. From left to right, it starts at the y-intercept zero, six and increases through the point ten, nine, the point twenty, eleven point five, and the point thirty, thirteen until it reaches a local maximum at fifty, sixteen. Then it decreases through the point sixty, fifteen point five, the point seventy, fourteen, the point eighty, fourteen, and the point one hundred, five. It continues decreasing through the x-intercept one hundred ten, zero, the point one hundred twenty, negative one, and the point one hundred forty, negative three point five until a local minimum at one hundred fifty, negative four. Then it increases though the point one hundred sixty, negative three point five and the x-intercept one hundred seventy, zero until it reaches a local maximum at one hundred seventy-eight, three point five. Then is decreases to one hundred eighty-five, three, and increases again to two hundred, six. The function is highlighted from x equals zero to x equals fifty.", "backgroundImage": {"height": 214, "url": "web+graphie:${☣ LOCALPATH}/images/4d0116921c7ff503390b93699e162cbfe44a1f2c", "width": 231}, "box": [231, 214], "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:-: | :-:\nRelative maximum or minimum | The coldest temperature outside the car was $-4^\\circ\\text{C}$.\nPositive or negative interval | Between the $110^\\text{th}$ and the $170^\\text{th}$ kilometers, the outside temperature was below zero.\nIncreasing or decreasing interval | Over the first $50\\text{ km}$, the temperature outside the car got warmer.", "images": {}, "replace": false, "widgets": {}}], "itemDataVersion": {"major": 0, "minor": 1}, "question": {"content": "Pedro went for a very long drive.\n\n$T(d)$ models the temperature (in degrees Celsius) outside Pedro's car as a function of the total distance he drove $d$ (in $\\text{km}$).\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 ten and is labeled d for the distance drove in kilometers. The y-axis scales by one and is labeled T of d for the temperature, in degrees Celsius, outside the car. The graph of the function is a continuous curve. From left to right, it starts at the y-intercept zero, six and increases through the point ten, nine, the point twenty, eleven point five, and the point thirty, thirteen until it reaches a local maximum at fifty, sixteen. Then it decreases through the point sixty, fifteen point five, the point seventy, fourteen, the point eighty, fourteen, and the point one hundred, five. It continues decreasing through the x-intercept one hundred ten, zero, the point one hundred twenty, negative one, and the point one hundred forty, negative three point five until a local minimum at one hundred fifty, negative four. Then it increases though the point one hundred sixty, negative three point five and the x-intercept one hundred seventy, zero until it reaches a local maximum at one hundred seventy-eight, three point five. Then is decreases to one hundred eighty-five, three, and increases again to two hundred, six.", "backgroundImage": {"height": 464, "url": "web+graphie:${☣ LOCALPATH}/images/08a39460df59acf57bd75ef5a4f0d20303e36c98", "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": ["Relative maximum or minimum", "Positive or negative interval", "Increasing or decreasing interval"], "orderMatters": false, "padding": true, "right": ["The coldest temperature outside the car was $-4^\\circ\\text{C}$.", "Between the $110^\\text{th}$ and the $170^\\text{th}$ kilometers, the outside temperature was below zero.", "Over the first $50\\text{ km}$, the temperature outside the car got warmer."]}, "static": false, "type": "matcher", "version": {"major": 0, "minor": 0}}}}}