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Graphing on a Number Line
Integers and real numbers can be represented on a number line. The point on this line associated with each number is called the graph of the number. Notice that number lines are spaced equally, or proportionately (see Figure 1).
Figure 1. Number lines.
Graphing inequalities
When graphing inequalities involving only integers, dots are used.
Example 1
Graph the set of x such that 1 ? x ? 4 and x is an integer (see Figure 2).
{ x:1 ? x ? 4, x is an integer}
Figure 2. A graph of {x:1 ? x ? 4, x is an integer}.
When graphing inequalities involving real numbers, lines, rays, and dots are used. A dot is used if the number is included. A hollow dot is used if the number is not included. Example 2
Graph as indicated (see Figure 3).
1.Graph the set of x such that x ? 1.
{ x: x ? 1}
2.Graph the set of x such that x > 1 (see Figure 4).
{ x: x > 1}
3.Graph the set of x such that x < 4 (see Figure 5).
{ x: x < 4}
This ray is often called an open ray or a half line. The hollow dot distinguishes an open ray from a ray.
Figure 3. A graph of { x: x ? 1}.
Figure 4. A graph of { x: x > 1}
Figure 5. A graph of { x: x < 4} Intervals
An interval consists of all the numbers that lie within two certain boundaries. If the two boundaries, or fixed numbers, are included, then the interval is called a closed interval. If the fixed numbers are not included, then the interval is called an open interval.Example 3
Graph.
1.Closed interval (see Figure 6).
{ x: -1 ? x ? 2}
2.Open interval (see Figure 7).
{ x: -2 < x < 2}
Figure 6. A graph showing closed interval { x: -1 ? x ? 2}.
Figure 7. A graph showing open interval { x: -2 < x < 2}.
If the interval includes only one of the boundaries, then it is called a half-open interval. Example 4
Graph the half-open interval (see Figure 8).
{ x: -1 < x ? 2}
Figure 8. A graph showing half-open interval { x: -1 < x ? 2}.
First you must use a graphing calculator.
Most graphing calculators graph functions, i.e. relations of the form y=f(x).
Some graphing calculators are able to graph equations (not necessarily functions). On one of these calculators your draw the vertical line x=-3, then you shade to the left of the point x=-3. That gives you the real line from infinity up to but not including x=-3.
Generally, people do not need calculators to find the solutions to inequalities in just one variable.
Error 07 Syntax
Means you made a typing error while entering the equation. Using the minus sign instead of the negation sign (change sign) (-), can produce a syntax error. Maybe you need to explicitly type the multiplication sign
y= (-) 1.5*x +3
Try entering it as 3 - 1.5*x
If you want to graph the absolute value of a function, feed the function to the absolute value ie graph y= abs(f(x)). The calculator will take care of it. See screen captures where I draw the function y1=x^3-5x^2-3 and y2='x^3-5x^2-3'. On the first graph the function is represented and on the second the function and its absolute value.
The calculator knows how to calculate the absolute value of an expression. The name of the command is abs(
First you must configure your calculator to perform 3D graphics Press MODE 1.The first line shown is Graph. Unfold the hidden menu list with the right arrow and choose Graph 5:3D 2. Press ENTER to validate.
Now you must define the surface you want to draw 1. Press the [diamond] key then [Y=] to get a list of function names, the first of which is z1 2. Enter the following function (or your own) z1=(x^3*y-y^3*x)/390 ( x cubed times y -y cubed times x) divided by 390. 3 Press ENTER.
Graph the function Press the [diamond] key then [GRAPH]
The graphing screen displays progress in %. When it is finished you will see a weird sombrero.
First you must configure your calculator to perform 3D graphics Press MODE 1.The first line shown is Graph. Unfold the hidden menu list with the right arrow and choose Graph 5:3D 2. Press ENTER to validate.
Now you must define the surface you want to draw 1. Press the [diamond] key then [Y=] to get a list of function names, the first of wich is z1 2. Enter the following function (or your own) z1=(x^3*y-y^3*x)/390 ( x cubed times y -y cubed times x) divided by 390. 3 Press ENTER.
Graph the function Press the [diamond] key then [GRAPH]
The graphing screen displays progess in %. When it is finished you will see a weird sombrero.
If either error occurs when trying to graph a function (not a STAT PLOT), the error can be corrected by turning off the STAT PLOTS. The following steps will turn the STAT PLOTS off, allowing the graph of the function to be displayed.• Press [2nd] [Y=] to access the STAT PLOTS menu.
• Select 4: PlotsOff.
• Press [ENTER].
• Try graphing a function like y = x^4-3x^3+6x-1
(1) if asking for graphing y= -2/3x+2, then press [diamond] [F1: Y=] type in .2/3x +2, see graph by [diamond][graph]
(2) if asking for graphing y= -2/3x+a, where a=3x, then first archive a=3x in Home screen by [home], type 3x [sto] a, then go back to y= menu, and type -2/3x+a in Y1
(3) if asking for graphing an equation that is dependent on 2 variables at the same time, use x-y-z axis (aka, change mode to graphing 3-D by [mode]graph [5:3D]) then enter desired equation in y= menu using Z function in terms of x and y aka z(x,y)= ...)
While the graph function menu is on the display press the F3 button to display the graph you want to do. Then press the function key that corresponds to the graph that you want.
If you have the manual it explains it on page 117. Kind of hard to explain it here when you can't type the buttons. LOL
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