{"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 $P(w)$ and the $y$-axis, which is the point on the graph where $w=0$. \n\nThe $y$-intercept in this graph is $(0,-250)$, which means that *if Jada doesn't sell anything, she loses $\\$250$.*\n\n\n\n[[☃ image 1]]\n\n", "images": {}, "replace": false, "widgets": {"image 1": {"alignment": "block", "graded": true, "options": {"alt": "The first and fourth quadrants of a coordinate plane. The x-axis scales by ten and is labeled w for the weight, in kilograms, of paprika sold over the week. The y-axis scales by one hundred and is labeled P of w for Jada's weekly profit in dollars. The graph of the function is a straight line. It starts at the y-intercept zero, negative two hundred fifty and increases through the x-intercept thirty-five, zero and goes through the point one hundred, five hundred. The point zero, negative two hundred fifty is plotted on the function.", "backgroundImage": {"height": 214, "url": "web+graphie:${☣ LOCALPATH}/images/4e83cdfd02f3a6fa261e85ea2aebd13cebb854e0", "width": 235}, "box": [235, 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 $P(w)>0$ over the interval $[35,\\infty)$, this is a positive interval. This means that *Jada needs to sell more than $\\textit{35}$ kilograms in order to make a profit.*\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 ten and is labeled w for the weight, in kilograms, of paprika sold over the week. The y-axis scales by one hundred and is labeled P of w for Jada's weekly profit in dollars. The graph of the function is a straight line. It starts at the y-intercept zero, negative two hundred fifty and increases through the x-intercept thirty-five, zero and goes through the point one hundred, five hundred. The function is highlighted after x equals thirty-five zero.", "backgroundImage": {"height": 214, "url": "web+graphie:${☣ LOCALPATH}/images/703ba7de82a746acf37b0585934b55b176b19a81", "width": 243}, "box": [243, 214], "caption": "", "labels": [], "range": [[0, 10], [0, 10]], "static": false, "title": ""}, "static": false, "type": "image", "version": {"major": 0, "minor": 0}}}}, {"content": "An increasing (or decreasing) interval is a domain interval over which the function values increase (or decrease) as the input variable increases.\n\nThis graph is always increasing. This means that *the more paprika Jada sells, the more profit she makes.*\n\n\n\n[[☃ image 1]]\n\n", "images": {}, "replace": false, "widgets": {"image 1": {"alignment": "block", "graded": true, "options": {"alt": "The first and fourth quadrants of a coordinate plane. The x-axis scales by ten and is labeled w for the weight, in kilograms, of paprika sold over the week. The y-axis scales by one hundred and is labeled P of w for Jada's weekly profit in dollars. The graph of the function is a straight line. It starts at the y-intercept zero, negative two hundred fifty and increases through the x-intercept thirty-five, zero and goes through the point one hundred, five hundred. The function is completely highlighted.", "backgroundImage": {"height": 214, "url": "web+graphie:${☣ LOCALPATH}/images/ce977796d4d37fd64cc2b4cce059995dc08d338c", "width": 243}, "box": [243, 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:-: | :-:\n$y$-intercept | If Jada doesn't sell anything, she loses $\\$250$.\nPositive or negative interval | Jada needs to sell more than $35$ kilograms in order to make a profit.\nIncreasing or decreasing interval | The more paprika Jada sells, the more profit she makes.", "images": {}, "replace": false, "widgets": {}}], "itemDataVersion": {"major": 0, "minor": 1}, "question": {"content": "Jada sells ground paprika.\n\n$P(w)$ models Jada's weekly profit (in dollars, where a negative profit means Jada lost money) as a function of the total weight of paprika $w$ she sold over that week (in kilograms).\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 five and is labeled w for the weight, in kilograms, of paprika sold over the week. The y-axis scales by fifty and is labeled P of w for Jada's weekly profit in dollars. The graph of the function is a straight line. It starts at the y-intercept zero, negative two hundred fifty and increases through the x-intercept thirty-five, zero and goes through the point one hundred, five hundred.", "backgroundImage": {"height": 440, "url": "web+graphie:${☣ LOCALPATH}/images/0f93aa8003ea982360459b7d07103ad8aab4a311", "width": 480}, "box": [480, 440], "caption": "", "labels": [], "range": [[0, 10], [0, 10]], "static": false, "title": ""}, "static": false, "type": "image", "version": {"major": 0, "minor": 0}}, "matcher 1": {"alignment": "default", "graded": true, "options": {"labels": ["**Feature**", "**Statement**"], "left": ["$y$-intercept", "Positive or negative interval", "Increasing or decreasing interval"], "orderMatters": false, "padding": true, "right": ["If Jada doesn't sell anything, she loses $\\$250$.", "Jada needs to sell more than $35$ kilograms in order to make a profit.", "The more paprika Jada sells, the more profit she makes."]}, "static": false, "type": "matcher", "version": {"major": 0, "minor": 0}}}}}