{"answerArea": {"calculator": false, "chi2Table": false, "periodicTable": false, "tTable": false, "zTable": false}, "hints": [{"content": "The $x$-intercept is the point of intersection between the graph of the function $W(t)$ and the $x$-axis, which is the point on the graph where $W(t)=0$. In this case the horizontal axis represents the variable $t$, but it's common to call that axis the $x$-axis.\n\nThis graph has an $x$-intercept at $(9,0)$, which means that *the plumber drained all the water out after $\\textit{9}$ hours.*\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 hours since the leak began. The y-axis scales by ten and is labeled W of t for the amount of water in the basement, in liters. The graph of the function is made up of a line segment and a curve. From left to right, it starts at the y-intercept zero, zero. A line segment connects zero, zero to five, seventy. Then the function decreases at a non linear rate through the point six point five, sixty-five, the point seven point five, fifty-six, and the point eight point five, twenty-five until stopping at the x-intercept nine, zero. The x-intercept nine, zero is plotted on the function.", "backgroundImage": {"height": 231, "url": "web+graphie:${☣ LOCALPATH}/images/4d64351a2e8c6370f8fb6d73c13d527dba530f5e", "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 $W(t)=70$, which means that *the amount of water reached $\\textit{70}$ liters before the draining began.*\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 hours since the leak began. The y-axis scales by ten and is labeled W of t for the amount of water in the basement, in liters. The graph of the function is made up of a line segment and a curve. From left to right, it starts at the y-intercept zero, zero. A line segment connects zero, zero to five, seventy. Then the function decreases at a non linear rate through the point six point five, sixty-five, the point seven point five, fifty-six, and the point eight point five, twenty-five until stopping at the x-intercept nine, zero. The point five, seventy is plotted on the function.", "backgroundImage": {"height": 231, "url": "web+graphie:${☣ LOCALPATH}/images/77a5ed26062b353a3c25081f193a082725cf9e22", "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 $[0,5]$ is an increasing interval. This means that *over the first $\\textit{5}$ hours, the leak just got bigger and bigger.*\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 hours since the leak began. The y-axis scales by ten and is labeled W of t for the amount of water in the basement, in liters. The graph of the function is made up of a line segment and a curve. From left to right, it starts at the y-intercept zero, zero. A line segment connects zero, zero to five, seventy. Then the function decreases at a non linear rate through the point six point five, sixty-five, the point seven point five, fifty-six, and the point eight point five, twenty-five until stopping at the x-intercept nine, zero. The function is highlighted from x equals zero to z equals five.", "backgroundImage": {"height": 231, "url": "web+graphie:${☣ LOCALPATH}/images/61ceed3c1c8b3f033028b0234851918625358a8b", "width": 231}, "box": [231, 231], "caption": "", "labels": [], "range": [[0, 10], [0, 10]], "static": false, "title": ""}, "static": false, "type": "image", "version": {"major": 0, "minor": 0}}}}, {"content": "To sum it up, the table should look as follows:\n\nFeature | Statement\n:-: | :-:\n$x$-intercept | The plumber drained all the water out after $9$ hours.\nRelative maximum or minimum | The amount of water reached $70$ liters before the draining began.\nIncreasing or decreasing interval | Over the first $5$ hours, the leak just got bigger and bigger.", "images": {}, "replace": false, "widgets": {}}], "itemDataVersion": {"major": 0, "minor": 1}, "question": {"content": "Dina discovered a water leak in her basement and called a plumber to fix and drain it.\n\n$W(t)$ models the amount of water in the basement (in liters) $t$ hours since the leak began.\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 zero point five and is labeled t for the number of hours since the leak began. The y-axis scales by five and is labeled W of t for the amount of water in the basement, in liters. The graph of the function is made up of a line segment and a curve. From left to right, it starts at the y-intercept zero, zero. A line segment connects zero, zero to five, seventy. Then the function decreases at a non linear rate through the point six point five, sixty-five, the point seven point five, fifty-six, and the point eight point five, twenty-five until stopping at the x-intercept nine, zero.", "backgroundImage": {"height": 464, "url": "web+graphie:${☣ LOCALPATH}/images/f09ef2ae43fd0ec7701ef0889821b1ccf2f480f1", "width": 464}, "box": [464, 464], "caption": "", "labels": [], "range": [[0, 10], [0, 10]], "static": false, "title": ""}, "static": false, "type": "image", "version": {"major": 0, "minor": 0}}, "matcher 1": {"alignment": "default", "graded": true, "options": {"labels": ["**Feature**", "**Statement**"], "left": ["$x$-intercept", "Relative maximum or minimum", "Increasing or decreasing interval"], "orderMatters": false, "padding": true, "right": ["The plumber drained all the water out after $9$ hours.", "The amount of water reached $70$ liters before the draining began.", "Over the first $5$ hours, the leak just got bigger and bigger."]}, "static": false, "type": "matcher", "version": {"major": 0, "minor": 0}}}}}