#### Mathematical Practices

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##### Sections
###### Monitoring Progress
Exercise name Free?
Monitoring Progress 1 A typical graphing calculator has a height to width ratio of 32​. Therefore, the graphing calculator will display a square window if the height and width satisfy this ratio. WidthHeight​=32​​ Let's find the height (y) and width (x) of the given viewing window. Height:Width:​7−(-3)=107−(-8)=15​ Now we can use our formula. WidthHeight​=32​Height=10, Width=151510​=?32​ba​=b/5a/5​32​=32​ Yes, the viewing window is a square.
Monitoring Progress 2 A typical graphing calculator has a height to width ratio of 32​. Therefore, the graphing calculator will display a square window if the height and width satisfy this ratio. WidthHeight​=32​ Let's find the height (y) and width (x) of the given viewing window. Height:Width:​9−(-9)=186−(-6)=12​ Now we can use our formula. WidthHeight​=32​Height=18, Width=121218​=?32​ba​=b/6a/6​23​​=32​ No, the viewing window is not a square.
Monitoring Progress 3 A typical graphing calculator has a height to width ratio of 32​. Therefore, the graphing calculator will display a square window if the height and width satisfy this ratio. WidthHeight​=32​ Let's find the height (y) and width (x) of the given viewing window. Height:Width:​12−(-12)=2418−(-18)=36​ Now we can use our formula. WidthHeight​=32​Height=24, Width=363624​=?32​ba​=b/12a/12​32​=32​ Yes, the viewing window is a square.
Monitoring Progress 4 To enter the equation, we press Y= on our calculator, and then write the equation on one of the rows.Next, by pressing GRAPH, the calculator will plot the equation using the standard viewing windowHowever, we want the fancy square viewing window. A non-square window just won't do. To view the window in a square format, we need to change the window so that WidthHeight​=32​. If we let -9≤x≤9 then -6≤y≤6 will result in a square window. To make this change, press the WINDOW button and make the necessary changes.Once more we press GRAPH, and the calculator will plot the graph using the new window settings.
Monitoring Progress 5 To enter the equation, we press Y= on our calculator, and then write the equation on one of the rows.Next, by pressing GRAPH, the calculator will plot the equation using the standard viewing windowHowever, we want the fancy square viewing window. A non-square window just won't do. To view the window in a square format, we need to change the window so that WidthHeight​=32​. If we let -9≤x≤9 then -6≤y≤6 will result in a square window. To make this change, press the WINDOW button and make the necessary changes.Once more we press GRAPH, and the calculator will plot the graph using the new window settings.
Monitoring Progress 6 To enter the equation, we press Y= on our calculator, and then write the equation on one of the rows.Next, by pressing GRAPH, the calculator will plot the equation using the standard viewing windowHowever, we want the fancy square viewing window. A non-square window just won't do. To view the window in a square format, we need to change the window so that WidthHeight​=32​. If we let -9≤x≤9 then -6≤y≤6 will result in a square window. To make this change, press the WINDOW button and make the necessary changes.Once more we press GRAPH, and the calculator will plot the graph using the new window settings.
Monitoring Progress 7 To enter the equation, we press Y= on our calculator, and then write the equation on one of the rows.Next, by pressing GRAPH, the calculator will plot the equation using the standard viewing windowHowever, we want the fancy square viewing window. A non-square window just won't do. To view the window in a square format, we need to change the window so that WidthHeight​=32​. If we let -9≤x≤9 then -6≤y≤6 will result in a square window. To make this change, press the WINDOW button and make the necessary changes.Once more we press GRAPH, and the calculator will plot the graph using the new window settings.
Monitoring Progress 8 To enter the equation, we press Y= on our calculator, and then write the equation on one of the rows.Next, by pressing GRAPH, the calculator will plot the equation using the standard viewing windowHowever, we want the fancy square viewing window. A non-square window just won't do. To view the window in a square format, we need to change the window so that WidthHeight​=32​. If we let -12≤x≤12 then -8≤y≤8 will result in a square window. To make this change, press the WINDOW button and make the necessary changes.Once more we press GRAPH, and the calculator will plot the graph using the new window settings.
Monitoring Progress 9 To enter the equation, we press Y= on our calculator, and then write the equation on one of the rows.Next, by pressing GRAPH, the calculator will plot the equation using the standard viewing windowHowever, we want the fancy square viewing window. A non-square window just won't do. To view the window in a square format, we need to change the window so that WidthHeight​=32​. If we let -9≤x≤9 then -6≤y≤6 will result in a square window. To make this change, press the WINDOW button and make the necessary changes.Once more we press GRAPH, and the calculator will plot the graph using the new window settings.
Monitoring Progress 10 Let's look at the graph of y=x in a standard viewing window.Next, let's change the viewing window so that it's a square. We can for example use -9≤x≤9 and -6≤y≤6 which results in a square viewing window.When using a square viewing window, it appears like the slope increases. This is however not the case. The slope is still the same but given the new graphs perspective, it looks like it is steeper.