{"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 $A(t)=-12$, which means that *Keith's lowest altitude was $\\textit{12}$ meters below the ground.*\n\n\n\n[[☃ image 1]]\n\n", "images": {}, "replace": false, "widgets": {"image 1": {"alignment": "block", "graded": true, "options": {"alt": "The first and fourth quadrants of a coordinate plane. The x-axis scales by one and is labeled t for the number of minutes. The y-axis scales by four and is labeled T of t for Keith's altitude in meters relative to the ground. The graph of the function is made up of line segments. From left to right, it starts at the y-intercept zero, eight. A line segment connects zero, eight to one, fourteen. A line segment connects one, fourteen to two, fourteen. A line segment connects two, fourteen to three, zero. A line segment connects three, zero to three point five, zero. A line segment connects three point five, zero to five, negative twelve. A line segment connects five, negative twelve to six point five, zero. A line segment connects six point five, zero to eight, twenty. A line segment connects eight, twenty to eight point five, fourteen. A line segment connects eight point five, fourteen to nine, fourteen. A line segment connects nine, fourteen to ten, zero. The point five, negative nine is plotted on the function.", "backgroundImage": {"height": 214, "url": "web+graphie:${☣ LOCALPATH}/images/9310b11a72d5e09598eccf806479da016f0c3b57", "width": 218}, "box": [218, 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 $A(t)>0$ over the interval $[6.5,10]$, this is a positive interval. This means that *between the $\\textit{6.5}$- and $\\textit{10}$-minute marks, Keith was above the ground.*\n\n\n\n[[☃ image 1]]\n\n", "images": {}, "replace": false, "widgets": {"image 1": {"alignment": "block", "graded": true, "options": {"alt": "The first and fourth quadrants of a coordinate plane. The x-axis scales by one and is labeled t for the number of minutes. The y-axis scales by four and is labeled T of t for Keith's altitude in meters relative to the ground. The graph of the function is made up of line segments. From left to right, it starts at the y-intercept zero, eight. A line segment connects zero, eight to one, fourteen. A line segment connects one, fourteen to two, fourteen. A line segment connects two, fourteen to three, zero. A line segment connects three, zero to three point five, zero. A line segment connects three point five, zero to five, negative twelve. A line segment connects five, negative twelve to six point five, zero. A line segment connects six point five, zero to eight, twenty. A line segment connects eight, twenty to eight point five, fourteen. A line segment connects eight point five, fourteen to nine, fourteen. A line segment connects nine, fourteen to ten, zero. The function is highlighted from x equals six point five to x equals ten.", "backgroundImage": {"height": 214, "url": "web+graphie:${☣ LOCALPATH}/images/0dd18b8059a93f70e78ca9924b03aa06888a5d96", "width": 218}, "box": [218, 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 $[5.5,8]$ is an increasing interval. This means that *between the $\\textit{5}$- and $\\textit{8}$-minute marks, the elevator was going up.*\n\n\n\n[[☃ image 1]]\n\n", "images": {}, "replace": false, "widgets": {"image 1": {"alignment": "block", "graded": true, "options": {"alt": "The first and fourth quadrants of a coordinate plane. The x-axis scales by one and is labeled t for the number of minutes. The y-axis scales by four and is labeled T of t for Keith's altitude in meters relative to the ground. The graph of the function is made up of line segments. From left to right, it starts at the y-intercept zero, eight. A line segment connects zero, eight to one, fourteen. A line segment connects one, fourteen to two, fourteen. A line segment connects two, fourteen to three, zero. A line segment connects three, zero to three point five, zero. A line segment connects three point five, zero to five, negative twelve. A line segment connects five, negative twelve to six point five, zero. A line segment connects six point five, zero to eight, twenty. A line segment connects eight, twenty to eight point five, fourteen. A line segment connects eight point five, fourteen to nine, fourteen. A line segment connects nine, fourteen to ten, zero. The function is highlighted from x equals five point five to x equals eight.", "backgroundImage": {"height": 214, "url": "web+graphie:${☣ LOCALPATH}/images/584530969e1659fc1a4ea2bdd8457c766b575394", "width": 218}, "box": [218, 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 | Keith's lowest altitude was $12$ meters below the ground.\nPositive or negative interval | Between the $6.5$- and $10$-minute marks, Keith was above the ground.\nIncreasing or decreasing interval | Between the $5$- and $8$-minute marks, the elevator was going up.", "images": {}, "replace": false, "widgets": {}}], "itemDataVersion": {"major": 0, "minor": 1}, "question": {"content": "Keith is an elevator operator in a big hotel.\n\n$A(t)$ models Keith's altitude (in meters relative to the ground) as a function of time (in minutes).\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 and fourth quadrants of a coordinate plane. The x-axis scales by zero point five and is labeled t for the number of minutes. The y-axis scales by two and is labeled T of t for Keith's altitude in meters relative to the ground. The graph of the function is made up of line segments. From left to right, it starts at the y-intercept zero, eight. A line segment connects zero, eight to one, fourteen. A line segment connects one, fourteen to two, fourteen. A line segment connects two, fourteen to three, zero. A line segment connects three, zero to three point five, zero. A line segment connects three point five, zero to five, negative twelve. A line segment connects five, negative twelve to six point five, zero. A line segment connects six point five, zero to eight, twenty. A line segment connects eight, twenty to eight point five, fourteen. A line segment connects eight point five, fourteen to nine, fourteen. A line segment connects nine, fourteen to ten, zero.", "backgroundImage": {"height": 440, "url": "web+graphie:${☣ LOCALPATH}/images/1b5f802683545267e6f8adb53a72872e39a74474", "width": 472}, "box": [472, 440], "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": ["Keith's lowest altitude was $12$ meters below the ground.", "Between the $6.5$- and $10$-minute marks, Keith was above the ground.", "Between the $5$- and $8$-minute marks, the elevator was going up."]}, "static": false, "type": "matcher", "version": {"major": 0, "minor": 0}}}}}