graphing
DESCRIPTION
Graphing. Module 5. Graphing. Viewing Window Size Graphing Equations Table Values X- and Y-Intercepts. Graphing. Viewing Window Size (Screen size) This key brings up the screen that controls the size of the viewing window. Graphing. Viewing Window Size. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Graphing](https://reader038.vdocuments.site/reader038/viewer/2022110403/56812be3550346895d905781/html5/thumbnails/1.jpg)
Graphing
Module 5
![Page 2: Graphing](https://reader038.vdocuments.site/reader038/viewer/2022110403/56812be3550346895d905781/html5/thumbnails/2.jpg)
GraphingViewing Window SizeGraphing EquationsTable ValuesX- and Y-Intercepts
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GraphingViewing Window Size (Screen size)
This key brings up the screen that controls the size of the viewing window.
![Page 4: Graphing](https://reader038.vdocuments.site/reader038/viewer/2022110403/56812be3550346895d905781/html5/thumbnails/4.jpg)
GraphingViewing Window Size
Xmin is the leftmost value on the x-axis
Xmax is the rightmost value on the x-axis
Xscl is the number of units between tick marks on the x-axis
Ymin is the lowest value on the y-axis
Ymax is the uppermost value on the y-axis
Yscl is the number of units between tick marks on the y-axis
Xres indicates how many pixels on the x-axis are skipped before another x-value is used to calculate y
![Page 5: Graphing](https://reader038.vdocuments.site/reader038/viewer/2022110403/56812be3550346895d905781/html5/thumbnails/5.jpg)
GraphingViewing Window Size
To change the window size, you can go down and manually enter the specific values to be changed or go to a preset screen size. To manually enter new values, move the cursor to where you want a new value and enter the new value.
![Page 6: Graphing](https://reader038.vdocuments.site/reader038/viewer/2022110403/56812be3550346895d905781/html5/thumbnails/6.jpg)
Graphing
To use the preset window values, you can change the viewing window by using the ZOOM menu.
Pressing the gives us other common window sizes.
![Page 7: Graphing](https://reader038.vdocuments.site/reader038/viewer/2022110403/56812be3550346895d905781/html5/thumbnails/7.jpg)
GraphingThe ZOOM MENU-
1:ZBox - allows you to draw a box around the part of the screen you want to see in the window.
2:Zoom In - magnifies the graph. You can change the center of the zoomed window by moving the cursor before pressing ENTER
(Preset window sizes)
![Page 8: Graphing](https://reader038.vdocuments.site/reader038/viewer/2022110403/56812be3550346895d905781/html5/thumbnails/8.jpg)
GraphingThe ZOOM MENU-
3:Zoom Out – shrinks the graph. You can change the center of the graph by moving the cursor before you press ENTER
4:Zdecimal-sets the window so that each pixel along the x-axis represents one tenth
(Preset window sizes)
![Page 9: Graphing](https://reader038.vdocuments.site/reader038/viewer/2022110403/56812be3550346895d905781/html5/thumbnails/9.jpg)
Graphing
5:Zsquare-sets the window so that the distance between tick marks on the x-axis is the same as the distance between tick marks on the y-axis
6:Zstandard-sets the window to the default window
(x’s go from –10 to 10;
Y’s go from –10 to 10)
![Page 10: Graphing](https://reader038.vdocuments.site/reader038/viewer/2022110403/56812be3550346895d905781/html5/thumbnails/10.jpg)
GraphingThe ZOOM MENU - (Preset window sizes)
7:ZTrig-sets the window to show two revolutions and the tick marks to represent multiples of 90
8:Zinteger-sets the window so that each pixel along the x-axis represents one
9:ZoomStat-fits the window to statistical data
![Page 11: Graphing](https://reader038.vdocuments.site/reader038/viewer/2022110403/56812be3550346895d905781/html5/thumbnails/11.jpg)
GraphingThe ZOOM MENU
0:ZoomFit-changes the window so that both the lowest and the highest values of y are shown in the window. This is often an extreme case of zooming in and out and you may lose details
6:ZStandard
0:ZoomFit
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GraphingThe ZOOM MENU - (Preset window sizes)
For most of the things we will do this semester, the Zoom 6:standard option will be the best window viewing size. You can choose this option by pressing
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GraphingGraphing Equations
In order to graph an equation (they will usually have an x and a y variable), the equation must be solved for y=
That is, y must be on a side by itself in order to enter it into the calculator.
Yes: y = 3x – 4 No: 2x + 3y = 6
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GraphingGraphing Equations
Graph the equation y = 3x – 4
Because we have y= form, this equation is ready to enter:
Press
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GraphingGraphing Equations
The window will show:
Then press
And the screen will show:
![Page 16: Graphing](https://reader038.vdocuments.site/reader038/viewer/2022110403/56812be3550346895d905781/html5/thumbnails/16.jpg)
Graphing
Graphing Equations
Graph 2x + 3y = 6
This equation is not ready to enter – why not???
You must first solve for y= form
and you will get y =
3
62 x
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Graphing
Graphing Equations
Now you are ready to enter y =
Press and enter the expression
Make sure you use parentheses in the numerator.
3
62 x
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GraphingGraphing Equations
The window will show:
Press
And the screen will show:
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GraphingGraphing Equations
The purpose for graphing an equation is to show graphically all solutions that the equation has. The graph consists of many, many ordered pairs of the form (x,y). Each of these ordered pairs is a solution to the equation.
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GraphingGraphing Equations
Often we find several ordered pairs that are solutions to an equation and use the points to determine what the graph looks like. Other times we will have the graph and need to identify specific points on the graph.
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GraphingGraphing Equations
Once you have the graph on the calculator window, specific points on the line can be found in a couple of different ways:
1. Using the key
2. Using a table of values
![Page 22: Graphing](https://reader038.vdocuments.site/reader038/viewer/2022110403/56812be3550346895d905781/html5/thumbnails/22.jpg)
GraphingThe key
Once you have the graph on the window, press to put the cursor on the line.
This will give you an x-value and a y-value.
For additional values, use the left and right arrow keys to move the cursor forward and back.
![Page 23: Graphing](https://reader038.vdocuments.site/reader038/viewer/2022110403/56812be3550346895d905781/html5/thumbnails/23.jpg)
GraphingThe key
In Zoom 6:standard mode, additional values will probably contain many decimal places, however, if you trace in Zoom 8:integer mode, “nicer” values will appear.
![Page 24: Graphing](https://reader038.vdocuments.site/reader038/viewer/2022110403/56812be3550346895d905781/html5/thumbnails/24.jpg)
ExampleGraph the line y = 3x – 4 and label at
least two points on the line.
In ZOOM 6:Standard
the window will show:
![Page 25: Graphing](https://reader038.vdocuments.site/reader038/viewer/2022110403/56812be3550346895d905781/html5/thumbnails/25.jpg)
ExampleTo find some specific points, press
The window will show:
This gives you one ordered pair that is a solution; that is, X = 0, Y = -4 denoted (0,-4).
![Page 26: Graphing](https://reader038.vdocuments.site/reader038/viewer/2022110403/56812be3550346895d905781/html5/thumbnails/26.jpg)
ExampleUse the left and right arrow keys to move the cursor around to different points on the line.
This will give you additional points, but they will
probably be UGLY.
(Remember, try the ZOOM 8:INTEGER mode to
get nicer looking numbers.)
![Page 27: Graphing](https://reader038.vdocuments.site/reader038/viewer/2022110403/56812be3550346895d905781/html5/thumbnails/27.jpg)
GraphingThe Table of Values
The second way to get specific points on the graph is to use the table of values.
In order to do this, you need to have the
equation entered as y1.
You can create a table for all values of x or for
particular values of x.
![Page 28: Graphing](https://reader038.vdocuments.site/reader038/viewer/2022110403/56812be3550346895d905781/html5/thumbnails/28.jpg)
GraphingThe Table of Values
The table of values will give you solutions to the
equation in a table format.
All of these ordered pair solutions will be points on the
line. So additional solutions are (-3, -13), (-1,-7), (2,2),…
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Graphing
The Table of Values
So,how do you get to the
TABLE of VALUES??
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Graphing
The Table of Values
Enter the equation as Y1:
Press to graph
Check your table settings
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Graphing
The Table of Values
Check your table settings
You will only need to do this the first time you want to automatically create a table, then you will be able to skip this step.
**See next screen for clarification.
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GraphingThe Table of Values
TblStart – tells where to start your values in the table
Tbl - tells how much to increase your x-values by each time
Independent – AUTO – will automatically compute your table without asking for specific x-values
Dependent – AUTO – will automatically compute the y-values for the given x-values
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GraphingThe Table of Values
NOTE: For typical table purposes, you will want Tbl to be 1 and both Independent and Dependent to be on AUTO. TblStart can be anything and can be adjusted later using the up and down arrows.
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GraphingThe Table of Values
Once the table is set up to your liking,
Press
Your window will show
You can get additional values by using the up and down arrow keys
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GraphingAdditional solutions
Example: For the equation y = 2x + 6, list five ordered pairs that are solutions.
Use either the trace key or the table of values…
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GraphingAdditional solutions
Example: For the equation y = 2x + 6, list five ordered pairs that are solutions.
Enter the equation as y=
View the table:
Solns: (-3,0), (-2,2), …
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GraphingX- and Y-Intercepts
Defn: The X-intercept is the point where the line crosses the x-axis.
Defn: The Y-intercept is the point where the line crosses the y-axis.
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GraphingX- and Y-Intercepts
The X- and Y-Intercepts are two points commonly used when labeling a graph.
We can use the calculator to find these two points.
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GraphingHow to find the Y-Intercept
Because the y-intercept is located on the y-axis, and because all points on the y-axis have an x coordinate of 0, we are going to calculate the value of y when x is 0.
Enter the equation as y= and graph Press
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GraphingFind the y-intercept of the equation
y = 3x – 4
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Graphing Enter the equation as y=
and graph
Press
To calculate 1:VALUE Press
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GraphingTo choose the x-value of 0
Press
This gives a y-value of -4, so the y-intercept is the ordered pair (0,-4).
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GraphingHow to find the X-Intercept
Because the x-intercept is located on the x-axis, and because all points on the x-axis have a y coordinate of 0, we are going to find where the y= equation is zero.
Enter the given equation as y1=
Enter y2 = 0 (Recall that y = 0 is the x-axis.) Graph Find where the equation (y1) intersects the x-axis (y2)
![Page 44: Graphing](https://reader038.vdocuments.site/reader038/viewer/2022110403/56812be3550346895d905781/html5/thumbnails/44.jpg)
GraphingFind the x-intercept of the equation
y = 3x – 4
![Page 45: Graphing](https://reader038.vdocuments.site/reader038/viewer/2022110403/56812be3550346895d905781/html5/thumbnails/45.jpg)
Graphing Enter the equation as
y1=
Enter y2 = 0
Graph
Calculate 5:intersect
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GraphingThen it gives you the x-value of 1.333333, which means the x-intercept is the ordered pair (1.33333,0).
![Page 47: Graphing](https://reader038.vdocuments.site/reader038/viewer/2022110403/56812be3550346895d905781/html5/thumbnails/47.jpg)
Graphing
DISCLAIMER:
All of the equations we will graph in Elementary Algebra will be lines that have at most 1 x-intercept
and at most 1 y-intercept. There are additional steps to be taken if there is more than one x-intercept.
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ExampleFind the x-intercept and the
y-intercept of the equation 43
2 xy
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ExampleFind the x-intercept and the y-intercept of the equation
Steps: Enter as y=
Graph
Find the x-intercept
Find the y-intercept
43
2 xy
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ExampleFind the x-int. and the y-int. of the
equation
Enter as y1=
Enter y2 = 0 Graph
43
2 xy
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ExampleFind the x-int. and the y-int. of the
equation
Your screens will look like this:
43
2 xy
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ExampleFind the x-intercept
(CALC 5:INTERSECT)
![Page 53: Graphing](https://reader038.vdocuments.site/reader038/viewer/2022110403/56812be3550346895d905781/html5/thumbnails/53.jpg)
ExampleFind the x-intercept
The x-intercept is the ordered pair (6,0)
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ExampleFind the y-intercept
(CALC 1:VALUE)
Enter the x value as 0
![Page 55: Graphing](https://reader038.vdocuments.site/reader038/viewer/2022110403/56812be3550346895d905781/html5/thumbnails/55.jpg)
ExampleFind the y-intercept
The y-intercept is the ordered pair (0,-4)