## Graphing Calculator Help

To graph functions, click on the Eqn tab.

From the Mode pulldown, select the type of function you wish to graph.

For f(x) function graphs, enter the functions you wish to graph, using x as the input variable.

For r(t) polar graphs, enter your equations, using t as the input variable, in place of θ.

For x(t),y(t) parametric graphs, enter your equations in pairs, using t as the input variable.

Once you have entered the functions, click the Plot Graphs button to plot the graphs and register the equations. You can now use these functions in the calculator, or generate a table of values for these functions

You can change the color of a graph by clicking the color box to the right of the function. Once you have selected the color you want, click Plot Graphs again to update the graph

To adjust the viewing window of the graph, you have several options:

• Click on the Window tab, and manually change the minimum and maximum x and y values, and for polar or parametric graphs, the minimum and maximum t values. Click Update after changing the values to update the graph, or Reset to reset the values back to the default.
• Hold down the Shift key as you click and drag the graph. This will allow you to pan (shift) the graphing window.
• Use your mouse wheel to zoom in and out while hovering the mouse pointer over the graph
• Use the navigation bar in the lower right corner of the graph to change the view. The + and - buttons zoom in and out, the o button resets the zoom, and the arrow buttons will pan (shift) the graphing window.

To calculate roots, maximums, minimums, and intersections, click on the Calc tab and select the item you want to calculate from the list. Note that this tab will only be available for f(x) function graphs.

#### Trace

Trace allows you to move a point along a curve. After selecting this option, click on the graph you want to trace. This will place a point on the graph which you can then drag along the graph. The approximate coordinates of the trace point will show next to the point.

#### Root / Zero

Root / Zero will find the location where a graph crosses the horizontal axis. If there are more than one graphs currently plotted, you will be asked to select which graph you want to find the root of; do so by clicking on the graph. Next, you will be asked to draw a box around the root. Click and drag on the graph to draw a box that encloses the root. The approximate coordinates of the root will be displayed.

#### Max and Min

Max and Min will find the location of a local maximum or minimum. If there are more than one graphs currently plotted, you will be asked to select which graph you want to find the max/min of; do so by clicking on the graph. Next, you will be asked to draw a box around the max/min. Click and drag on the graph to draw a box that encloses the max/min. The approximate coordinates of the max/min will be displayed.

#### Intersection

Intersection will find the location where two graphs cross. If there are more than two graphs currently plotted, you will be asked to select which graphs you want to find the intersection of; do so by clicking the two graphs. Next, you will be asked to draw a box around the intersection. Click and drag on the graph to draw a box that encloses the intersection. The approximate coordinates of the intersection will be displayed.

#### Derivative

Derivative will approximate the slope of the tangent line to a curve at a point. You will be asked to select which graph you want to work with; do so by clicking on the graph. You will be prompted for the x-value where you want to calculate the derivative. Enter it and hit Calculate. The approximate derivative will display.

#### Integral

Integral will approximate the area under a curve over an interval. You will be asked to select which graph you want to work with; do so by clicking on the graph. You will be prompted for the starting and ending x-valuex for the interval over which you want to find the integral. Enter these values and and hit calculate. The approximate integral will display.

To generate a table of values for the graphed functions, click on the Table tab. You have two options for the x-values: Ask or Auto

If you select Ask and click Go, a table will be generated with empty input boxes for the x values. You can manually enter the x-values you want to evaluate the functions at, and when you click or tab to the next box, the output values will automatically be calculated.

If you select Auto, then enter a starting x value and the step size - how far apart each consecutive x value should be. For example, if you select a start of 3 and a step of 2, then the table will be generated for x = 3, 5, 7, 9, etc. Click Go to generate the table.

In the lower left side of the screen you will find a box with a blue stripe. This is the output log. In addition to recording any calculated roots, max/mins, etc., you can also do calculations. In the entry box below the output log, type any numerical expression and click Enter or press Enter of your keyboard. The result of the calculation will display in the output log.

If you have graphed functions, you can evaluate the functions in the calculator. For example, entering f(3) will evaluate the graphed f(x) function at x=3.

If you want to edit a previous calculation, click the line number to the left of the expression to copy that expression back into the input box. Alternatively, you can use the up and down arrow keys to navigate through previous input expressions.

If you want to use the results of previous calculations in your next calculation, you can do that:

• ## or ANS will use the result of the last calculation
• #linenumber, like #2, will use the result from that line
• #2x or #2y will allow you to access the x or y coordinate, respectively, from a previous calculation on a graph that produced a point.

These functions and constants can be used in graph equations or in the calculator

• pi: The mathematical constant pi
• e: The mathematical constant e
• 3^2: Exponent 32
• sqrt(5): Square root
• root(3)(5): Cube root
• abs(4): Absolute value
• sin, cos, tan, sec, csc, cot: The trig functions. The calculator always operates in radian mode
• arcsin, arccos, arctan, arcsec, arccsc, arccot: The inverse trig functions
• log(3): The common log (base 10)
• ln(3): The natural log (base e)

Statistical functions:

• 4!: Factorial
• nCr(n,r) and nPr(n,r) Combinations and permutations of n objects taken r at a time.
• normalcdf(a,b,[mean,stdev]) Calculates the normal distribution probability P(a<x<b). Can optionally specify the mean and standard deviation, otherwise a standard normal distribution is used (mean=0, stdev=1).
• invnorm(p,[mean,stdev]) Finds the z score of the standard normal distribution so that the area to the left of this z score equals p. Can optionally specify the mean and standard deviation to find the x score so that the area to the left of this x score equals p.
• tcdf(a,b,df) Calculated the Student's t distribution probability P(a<x<b) with df degrees of freedom.
• invT(p,df) Finds the t score so that the area to the left of this t score equals p.
• binompdf(n,p,r) Finds the binomial probability P(X=r), the probability of r successes out of n trials, where each independent trial has probability of success of p.
• binomcdf(n,p,r) Like the binompdf, but finds the probability P(X≤r), the probably of at most r successes.