Graphing

Graphing

Module 5

GraphingViewing Window SizeGraphing EquationsTable ValuesX- and Y-Intercepts

GraphingViewing Window Size (Screen size)

This key brings up the screen that controls the size of the viewing window.

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

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.

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.

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)

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)

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)

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

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

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

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


Graph the equation y = 3x – 4

Because we have y= form, this equation is ready to enter:

Press


The window will show:

Then press

And the screen will show:

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

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



Press

And the screen will show:


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.


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.


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

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.

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.

ExampleGraph the line y = 3x – 4 and label at

least two points on the line.

In ZOOM 6:Standard

the window will show:

ExampleTo find some specific points, press


This gives you one ordered pair that is a solution; that is, X = 0, Y = -4 denoted (0,-4).

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.)

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.


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),…

Graphing

The Table of Values

So,how do you get to the

TABLE of VALUES??

Graphing

The Table of Values

Enter the equation as Y1:

Press to graph

Check your table settings

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.


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


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.


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

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…

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), …

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.

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.

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

GraphingFind the y-intercept of the equation

y = 3x – 4

Graphing Enter the equation as y=

and graph

Press

To calculate 1:VALUE Press

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).

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)

GraphingFind the x-intercept of the equation

y = 3x – 4

Graphing Enter the equation as

y1=

Enter y2 = 0

Graph

Calculate 5:intersect

GraphingThen it gives you the x-value of 1.333333, which means the x-intercept is the ordered pair (1.33333,0).

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.

ExampleFind the x-intercept and the

y-intercept of the equation 43

2 xy

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

ExampleFind the x-int. and the y-int. of the

equation

Enter as y1=

Enter y2 = 0 Graph

43

2 xy

ExampleFind the x-int. and the y-int. of the

equation

Your screens will look like this:

43

2 xy

ExampleFind the x-intercept

(CALC 5:INTERSECT)

ExampleFind the x-intercept

The x-intercept is the ordered pair (6,0)

ExampleFind the y-intercept

(CALC 1:VALUE)

Enter the x value as 0

ExampleFind the y-intercept

The y-intercept is the ordered pair (0,-4)

Documents

Graphing