{"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 $H(t)$ and the $y$-axis, which is the point on the graph where $t=0$. \n\nThe $y$-intercept in this graph is $(0,30)$, which means that *at the beginning, the surface's height was $\\textit{30}$ centimeters.*\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 two and is labeled t for the number of seconds. The y-axis scales by four and is labeled H of t for the height of the water. The graph of the function is a continuous curve. From left to right, it starts at the y-intercept zero, thirty, then it decreases through the point two, twenty-two until a local minimum at three, eighteen. Then it increases through the point four, twenty-two and the point five, twenty-eight until a local maximum at six, thirty-two. Then it decreases through the point seven, twenty-eight and the point eight, twenty-two until the local maximum at nine, twenty. Then it increases through the point ten, twenty-two and the point eleven, twenty-eight until the local maximum at twelve, thirty-four. Then it decreases through the point thirteen, twenty-eight and fourteen, twenty until a local minimum at fifteen, sixteen. Then it increases through the point sixteen, twenty and the point seventeen, twenty-eight until a local maximum at eighteen, thirty. Then it decreases through the point nineteen, twenty-seven. The y-intercept zero, thirty is plotted on the function.", "backgroundImage": {"height": 231, "url": "web+graphie:${☣ LOCALPATH}/images/04e9ec2b280027c5aed7590bc91a1a84f822cf23", "width": 214}, "box": [214, 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 at $t=6$, which means that *the water was at a crest after $\\textit{6}$ seconds.*\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 two and is labeled t for the number of seconds. The y-axis scales by four and is labeled H of t for the height of the water. The graph of the function is a continuous curve. From left to right, it starts at the y-intercept zero, thirty, then it decreases through the point two, twenty-two until a local minimum at three, eighteen. Then it increases through the point four, twenty-two and the point five, twenty-eight until a local maximum at six, thirty-two. Then it decreases through the point seven, twenty-eight and the point eight, twenty-two until the local maximum at nine, twenty. Then it increases through the point ten, twenty-two and the point eleven, twenty-eight until the local maximum at twelve, thirty-four. Then it decreases through the point thirteen, twenty-eight and fourteen, twenty until a local minimum at fifteen, sixteen. Then it increases through the point sixteen, twenty and the point seventeen, twenty-eight until a local maximum at eighteen, thirty. Then it decreases through the point nineteen, twenty-seven. The local maximum six, thirty-two is plotted on the function.", "backgroundImage": {"height": 231, "url": "web+graphie:${☣ LOCALPATH}/images/162d935570f25c8971fb6681a29fa617f11bdc8a", "width": 214}, "box": [214, 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 $[12,15]$ is a decreasing interval. This means that *the surface descended between $\\textit{12}$ and $\\textit{15}$ seconds.*\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 one and is labeled t for the number of seconds. The y-axis scales by two and is labeled H of t for the height of the water. The graph of the function is a continuous curve. From left to right, it starts at the y-intercept zero, thirty, then it decreases through the point two, twenty-two until a local minimum at three, eighteen. Then it increases through the point four, twenty-two and the point five, twenty-eight until a local maximum at six, thirty-two. Then it decreases through the point seven, twenty-eight and the point eight, twenty-two until the local maximum at nine, twenty. Then it increases through the point ten, twenty-two and the point eleven, twenty-eight until the local maximum at twelve, thirty-four. Then it decreases through the point thirteen, twenty-eight and fourteen, twenty until a local minimum at fifteen, sixteen. Then it increases through the point sixteen, twenty and the point seventeen, twenty-eight until a local maximum at eighteen, thirty. Then it decreases through the point nineteen, twenty-seven. The function is highlighted from x equals twelve to x equals fifteen.", "backgroundImage": {"height": 231, "url": "web+graphie:${☣ LOCALPATH}/images/3246c136962f76833fe832dc66b9ce3ebd6ccadf", "width": 214}, "box": [214, 231], "caption": "", "labels": [], "range": [[0, 10], [0, 10]], "static": false, "title": ""}, "static": false, "type": "image", "version": {"major": 0, "minor": 0}}}}, {"content": "To sum it up, the table should look as follows:\n\nFeature | Statement\n:-: | :-:\n$y$-intercept | At the beginning, the surface's height was $30$ centimeters.\nRelative maximum or minimum | The water was at a crest after $6$ seconds.\nIncreasing or decreasing interval | The surface descended between $12$ and $15$ seconds.", "images": {}, "replace": false, "widgets": {}}], "itemDataVersion": {"major": 0, "minor": 1}, "question": {"content": "Archimedes is making waves as he showers in his bath.\n\n$H(t)$ models the height (in centimeters) of the water as a function of time (in seconds).\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 two and is labeled t for the number of seconds. The y-axis scales by four and is labeled H of t for the height of the water. The graph of the function is a continuous curve. From left to right, it starts at the y-intercept zero, thirty, then it decreases through the point two, twenty-two until a local minimum at three, eighteen. Then it increases through the point four, twenty-two and the point five, twenty-eight until a local maximum at six, thirty-two. Then it decreases through the point seven, twenty-eight and the point eight, twenty-two until the local maximum at nine, twenty. Then it increases through the point ten, twenty-two and the point eleven, twenty-eight until the local maximum at twelve, thirty-four. Then it decreases through the point thirteen, twenty-eight and fourteen, twenty until a local minimum at fifteen, sixteen. Then it increases through the point sixteen, twenty and the point seventeen, twenty-eight until a local maximum at eighteen, thirty. Then it decreases through the point nineteen, twenty-seven.", "backgroundImage": {"height": 464, "url": "web+graphie:${☣ LOCALPATH}/images/ae4b5ca076a672e6d6512bd594fb83690f6a7122", "width": 464}, "box": [464, 464], "caption": "", "labels": [], "range": [[0, 10], [0, 10]], "static": false, "title": ""}, "static": false, "type": "image", "version": {"major": 0, "minor": 0}}, "matcher 1": {"alignment": "default", "graded": true, "options": {"labels": ["**Feature**", "**Statement**"], "left": ["$y$-intercept", "Relative maximum or minimum", "Increasing or decreasing interval"], "orderMatters": false, "padding": true, "right": ["At the beginning, the surface's height was $30$ centimeters.", "The water was at a crest after $6$ seconds.", "The surface descended between $12$ and $15$ seconds."]}, "static": false, "type": "matcher", "version": {"major": 0, "minor": 0}}}}}