{"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 $E(c)$ and the $x$-axis, which is the point on the graph where $E(c)=0$. In this case the horizontal axis represents the variable $c$, but it's common to call that axis the $x$-axis.\n\nThis graph has an $x$-intercept at $(3,0)$, which means that *the motor loses all efficiency when the current hits $\\textit{3}$ amperes.*\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 zero point five and is labeled c for the power input's current in amperes. The y-axis scales by ten and is labeled E of c for the efficiency in percentage points of a motor. The graph of the function is a continuous curve. From left to right, it starts at the x-intercept zero point four, zero and increases through the point zero point five, thirty and the point zero point seven-five, forty-eight until a local maximum at zero point nine, fifty where it stalls slightly. The function decreases from the point one, fifty  through the point two, thirty to the x-intercept three, zero. All values are estimates. The point three, zero is plotted on the function.", "backgroundImage": {"height": 218, "url": "web+graphie:${☣ LOCALPATH}/images/2315b2ce629572db5c5424a782ca0ee8a4b490e4", "width": 221}, "box": [221, 218], "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 $E(c)\\approx 50$, which means that *at its most efficient, the motor uses about $\\textit{50%}$ of the input power.*\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 zero point five and is labeled c for the power input's current in amperes. The y-axis scales by ten and is labeled E of c for the efficiency in percentage points of a motor. The graph of the function is a continuous curve. From left to right, it starts at the x-intercept zero point four, zero and increases through the point zero point five, thirty and the point zero point seven-five, forty-eight until a local maximum at zero point nine, fifty where it stalls slightly. The function decreases from the point one, fifty  through the point two, thirty to the x-intercept three, zero. All values are estimates. The point zero point nine, fifty is plotted on the function.", "backgroundImage": {"height": 226, "url": "web+graphie:${☣ LOCALPATH}/images/a6989ac6a72aa7e5cd0bd618f59e9efc479b3bde", "width": 221}, "box": [221, 226], "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 $[1,3]$ is a decreasing interval. This means that *as the input power's current grows beyond $\\textit 1$ ampere, the motor becomes less efficient.*\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 zero point five and is labeled c for the power input's current in amperes. The y-axis scales by ten and is labeled E of c for the efficiency in percentage points of a motor. The graph of the function is a continuous curve. From left to right, it starts at the x-intercept zero point four, zero and increases through the point zero point five, thirty and the point zero point seven-five, forty-eight until a local maximum at zero point nine, fifty where it stalls slightly. The function decreases from the point one, fifty through the point two, thirty to the x-intercept three, zero. All values are estimates. The function is highlighted from x equals one to x equals three.", "backgroundImage": {"height": 226, "url": "web+graphie:${☣ LOCALPATH}/images/16c3527def3cb3e26661f1c78cf37d0eb93b00ff", "width": 221}, "box": [221, 226], "caption": "", "labels": [], "range": [[0, 10], [0, 10]], "static": false, "title": ""}, "static": false, "type": "image", "version": {"major": 0, "minor": 0}}}}, {"content": "To sum it up, the table should look as follows:\n\nFeature | Statement\n:-: | :-:\n$x$-intercept | The motor loses all efficiency when the current hits $3$ amperes.\nRelative maximum or minimum | At its most efficient, the motor uses about $50\\%$ of the input power.\nIncreasing or decreasing interval | As the input power's current grows beyond $1$ ampere, the motor becomes less efficient.", "images": {}, "replace": false, "widgets": {}}], "itemDataVersion": {"major": 0, "minor": 1}, "question": {"content": "The efficiency of a motor can be measured by the percentage of the input power that the motor uses.\n\n$E(c)$ models the efficiency (in percentage points) of a certain motor as a function of the power input's current $c$ (in amperes).\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 two-five and is labeled c for the power input's current in amperes. The y-axis scales by five and is labeled E of c for the efficiency in percentage points of a motor. The graph of the function is a continuous curve. From left to right, it starts at the x-intercept zero point four, zero and increases through the point zero point five, thirty and the point zero point seven-five, forty-eight until a local maximum at zero point nine, fifty where it stalls slightly. The function decreases from the point one, fifty through the point two, thirty to the x-intercept three, zero. All values are estimates.", "backgroundImage": {"height": 472, "url": "web+graphie:${☣ LOCALPATH}/images/8749ab58c0504173be9d14824e3accfad42ee6d8", "width": 464}, "box": [464, 472], "caption": "", "labels": [], "range": [[0, 10], [0, 10]], "static": false, "title": ""}, "static": false, "type": "image", "version": {"major": 0, "minor": 0}}, "matcher 1": {"alignment": "default", "graded": true, "options": {"labels": ["**Feature**", "**Statement**"], "left": ["$x$-intercept", "Relative maximum or minimum", "Increasing or decreasing interval"], "orderMatters": false, "padding": true, "right": ["The motor loses all efficiency when the current hits $3$ amperes.", "At its most efficient, the motor uses about $50\\%$ of the input power.", "As the input power's current grows beyond $1$ ampere, the motor becomes less efficient."]}, "static": false, "type": "matcher", "version": {"major": 0, "minor": 0}}}}}