To enter the Grapher application, highlight the app using the directional keys. Press the ok key to enter the application. This application allows you to view the graph of a function, curve, conic and inequality, view the coordinates of your points, determine key characteristics, and consult a table of values.
To plot a graph or curve, you must first enter the expression. To enter your expression:
The graph or curve will appear in the Graph tab.
You can begin entering the expression of your function immediately upon entering the Grapher application.
The table of values for an expression can be found in the Table tab. There are two ways to access it.
First option: From the Expressions tab
The table of values is displayed.
Second option: From any tab
The table of values is displayed.
You can add several types of elements to the list of expressions: functions, inequalities, polar curves, conics and more. To add an element:
You can also create a function in the Calculation application. See the Variables section.
You can change an expression in the list by highlighting it and pressing the ok key.
The expression can now be edited and you can use the left and right keys to move the cursor within the expression.
For function composition, use the name of an existing function in the function expression. An example of a possible expression: $cos(f(x))$.
It is possible to change the plotting domain of a function or curve to restrict its plotted domain. To do so:
-10
for Xmin and 10
for XmaxOnce you have selected the values for your desired plot restriction, the curve or graph in the Graph tab will only be visible within the bounds you have set.
To plot a point, use the Point template or add an expression in the form (2,3)
.
To plot a list of points, use the List of points template or add an expression in the form {(2,3),(3,5)}
It is also possible to plot a list of points using a saved list or dataset from the Regression application. For example, $(X1,Y1)$ will plot the points using the
X1
andY1
lists in the Regression application.
To add an inverse function, add an expression that is a function of $y$. For example, $x = sin(y)$
It is also possible to graph the inverse of a function that is already defined. For example, if $f(x)$ is defined, you can graph its inverse by adding the expression $x=f(y)$.
To add a piecewise function, use the Piecewise function template and enter the desired expressions and domains.
Logic statements can be used in the domain field of a piecewise function and are available in the Logic section of the Toolbox.
It is possible to work with polar and parametric curves in the Grapher application without changing the mode of the calculator.
The expression of a polar function requires use of the θ symbol as a variable. This symbol can be entered by pressing the xnt key.
The expression of a parametric function needs to be typed as a column vector of size 2. The first component is the expression of x(t)
while the second component is the expression of y(t)
.
Templates for polar and parametric curves are available once Add an element has been selected.
To add an inequality, use the Inequality template and enter the desired expression. You can also create an inequality using the following symbols.
<
: shift followed by root>
: shift followed by square≤
: Open the toolbox and select ≤
≥
: Open the toolbox and select ≥
The “less than or equal to” symbol can also be entered by first inputting the
<
symbol followed by the=
symbol.
You can disable an element without deleting it from the expression list. When you disable an element, it will appear in gray in the expression list. You can edit the expression, but its graph and table of values will not appear in the Graph and Table tabs. To disable an element:
You can delete an element from the expression list. To delete the element:
You can also delete an element within the menu opened with the three dots to the right of the expression.
You can change the name of a function on the expression list. To rename a function:
When you add a new element, a color is automatically assigned and will be used when plotting the expression. To change the color:
For conic sections and linear expressions, it is possible to view additional details calculated from the expression (eccentricity, semi-major axis, slope, etc.)
When you first view the graph of an expression, the selected curve automatically shows points of interest in black. Interesting points include maximums, minimums, intercepts and intersections.
You can adjust the display window in the Graph tab to fit your needs. This includes: editing your X and Y values, zooming in and out, and more. There are three menus that allow you to adjust your graphing window: Auto, Axes and Navigate. To adjust your graphing window:
The NumWorks graphing calculator will adapt to display the best possible view of your curve. Once you enter your function, the resulting axes will be chosen automatically. When Auto is active, a yellow circle will appear to the right of its name. Once you exit this window, either with the directional keys or by changing the settings, Auto will be disabled and the yellow circle will disappear.
You can also highlight Auto and press the ok key to disabled the Auto mode.
The Axes menu allows you to make manual changes to the axes of your graphing window. To make changes to the X or Y values:
You can make your axes equal inside the Axes menu. To do this, highlight Make axes equal and confirm with the ok key. Selecting this option will lengthen the shortest axis to match the longest. When your axes are not equal, a symbol will appear beside the Axes menu.
Select Navigate to work with the interactive display window:
You can press plus and minus at anytime while in the Graph tab to zoom in/out.
You can move the cursor using the four directional arrows:
When tracing a curve, the cursor automatically snaps to interest points and the legend indicates what kind of point it is.
You can view the coordinates of any point on the graph. This information will appear in the legend at the bottom of the screen.
To select a specific point given an x-value:
You can also enter the value of X directly in the graphing window. To enter a negative value, first enter the number and then add the negative symbol before it.
To select a specific point given an y-value:
You can also Find X given Y in the Find menu.
You can view the value of a derivative of a function at a point on your curve.
If you would like to no longer display the value of the derivative of a function at a point, repeat these steps.
The Find menu allows you to find x given y, identify intersection points, minima and maxima and zeros, draw tangents with their equation and calculate integrals and area between curves. To locate the Find menu:
You can now choose which value you would like to discover. Use the updown keys to scroll through the menu and the ok key to select.
To determine the X value for a given Y value, use the Find X given Y feature. Enter the desired Y value and Confirm.
The cursor is now at the point with the Y value you requested. If multiple points exist for your Y value, you can navigate between them with the rightleft keys.
For the inverse image to be found the point must be located in the current graphing window.
You can find the intersection of two functions. The Intersection option will appear only if you are working with two or more functions. Highlight Intersection and press the ok key.
The cursor is now at the point where your curves intersect. If multiple intersection points exist, you can navigate between them with the rightleft keys.
You can find the maximum and minimum of your function. Highlight either Maximum or Minimum and press the ok key.
The cursor is now at the maximum/minimum point. If multiple minimum/maximum points exist, you can navigate between them with the rightleft keys.
You can find the point(s) where the value of your function is zero. Highlight Zeros and press the ok key.
The cursor is now at a point where the value of the selected function is zero. If multiple zeros exist, you can navigate between them with the rightleft keys.
You can observe the line tangent to the curve at a point. Highlight Tangent and press the ok key. The line tangent to your selected point will appear. Use the directional arrows to change the point or manually enter the X value of the point using the keyboard. The equation of the tangent line is given in the legend at the bottom of the screen.
You can evaluate an integral. To obtain the value of an integral:
Press the ok key if you wish to exit the Integral mode.
If more than one function is plotted, you can find the area between curves. To compute the area between curves:
When you enter the Table tab, $x$ values will automatically range from 0-10. There will be a column for the values of f(x) at a given x value. There will be a column for each function you enter.
You can fill the table of values with values of $x$ in any interval of your choice. To do this:
You can also highlight the x cell and press the ok key to enter the Set the interval menu.
You can manually enter values into the x column and receive the corresponding values in the f(x) column. Highlight the cell you wish to change and enter your desired value with the numeric keys. Confirm by pressing the ok key.
You can delete single rows as well as the entire first column. To delete a row, highlight the row you wish to delete and press the del key.
To delete the column of $x$ values:
You can display the exact values of the output of each expression instead of decimal approximations. To view exact values:
You can display a column of derivative function values in the table. To view this column:
If you would no longer like to view the derivative function column, highlight the first cell of the column and press the ok key. Highlight Hide derivative function and press the ok key. The derivative function column is no longer displayed.