Features and Calculator Skills Used for Elementary & Intermediate Algebra

Basic Things to Know:
·2ndQUIT returns user to the home screen.
·The blue arrows (up, down, left, right) allow you to navigate the screen.
·Lighten the screen using 2nd, the down arrow.
·Darken the screen using 2nd, the up arrow.
·CLEAR clears the home screen. Clear graphs of functions by using CLEAR to clear functions in the Y= window and clear graphs of vertical lines or circles by using ClrDraw in the DRAW menu.
·2ndMEM can be used to Reset the calculator to its default settings.

Common User Mistakes:
·Incorrectly using the gray negative (-) key for subtraction (the blue – key) or vice versa
·No image on  the screen-try darkening the screen
·A rational exponent requires a parenthesis for correct calculation

Example:
           
·More than one term in numerators and/or denominators requires parentheses, more than one term in radicands requires parentheses (when in doubt, use parentheses)
·All sets of parentheses must be closed
·Inappropriate MODE settings
·The  key does not enter x-squared on your screen. It merely squares a number or a variable that is already entered. For x-squared, press the  key and then press the  key.
·Inappropriate WINDOW settings to view graphs.
·The GRAPH feature will NOT graph if  Plot1  Plot 2  or  Plot 3 are selected (indicated by item being highlighted) in the Y= window. To unselect, move cursor to the Plot item that is highlighted and press ENTER. This unselects the item.

Menus:
·MODE

These are the general settings for MODE. Some exceptions you may encounter are (1) when graphing rational functions having vertical asymptotes, may be instructed to use DOT view instead of CONNECTED view to show that the vertical asymptotes are not a part of the graph and (2) for operations with complex numbers, use a+bi instead of REAL mode.

·WINDOW

These are the standard settings for WINDOW. These settings are used to adjust the graphing window as needed for the optimal view of a graph. Students may often need to change the settings for the Xmin, Xmax, and/or Ymin, Ymax to get a better look at a graph. In general, leave all other settings at 1.

·TBLSET

This menu allows you to set the TblStart for the minimum x-value in the table, and it allows you to set the increments between x-values in the table.

·ZOOM

The ZOOM menu is used for better viewing of graphs. For example, the user may need to Zoom In or Zoom Out to get the graph in the viewing window. ZBox lets you define a portion of the graph for a closer look at that part of the graph. ZDecimal replots the graph immediately using the WINDOW settings shown below.

Zstandard replots the functions immediately by changing WINDOW back to the standard settings. Zinteger lets you move the cursor to the point where you want the center of the window to be and then replots the graphs accordingly with an Xscl and Yscl of 10 each. ZoomFit is the menu item probably most often used by students. This feature replots the graphs immediately, recalculating the Ymin and Ymax to include the minimum and maximum values of the functions in the viewing window. However, Xmin and Xmax are NOT changed.

·TABLE
Example:

Shows the table values for the functions entered into the Y= window. In the example above, the functions that are entered are shown in the Y= window below.

TABLE is very useful as a tool for verification. By comparing values in a TABLE, students can verify that they have factored correctly or that they have simplified a rational expression correctly. TABLE can also be used to determine or verify what values are NOT in the domain of a given function.

·CALC

The menu in CALC will be used by students to find the intersection of 2 graphed functions, to find the zeros of a graphed function, to find the minimum or the maximum of a quadratic function, and to find the value of the function for the x-value that you choose.

·MATH

Under the heading MATH, the menu lets you, among other things, to convert a decimal number to a fraction (#1), to convert a fraction to a decimal (#2), to cube a number (#3), to take a cube root (#4), to take the xth root (#5), and to use the solver (#0 at the bottom of the list).
Under the heading NUM

the menu allows you to take the absolute value of a number (#1), to round a number to a specified number of decimal places (#2), to find the lcm of two numbers (#8), and to find the gcd of two numbers (#9).
Under the heading CPX

the menu allows you to find the conjugate of a complex number (#1), and to find the real part (#2) and the imaginary part (#3) of a complex number.

·DRAW

Under the DRAW heading, the menu allows you to draw vertical lines (#4), tangent lines (#5), inverse functions (#8), and circles (#9). You will have to clear by using ClrDraw (#1).

The POINTS heading,

can be used to plot points (#1) and to then remove plotted points (#2).

·TRACE
Use this feature to move to points on a graph, such as points of intersection. A common use for TRACE is to move the cursor to enter a Left Bound and a Right Bound when finding the zeros of a function.

·TEST

Use this menu to test comparisons of functions (useful for inequalities with absolute value) which are entered using

·VARS

entering (#1) Function and selecting the function from the list


Calculator Exercises:
1. Enter the functions in the Y= window as shown and GRAPH.

What change(s) would you recommend to make to the WINDOW settings in order to view the vertex of the parabola? Make the change(s) and GRAPH. Did this present a view of the vertex?

2. What common mistake do students make when asked to expand the expression
?  Use TABLE to show students that .
Enter the expressions on either side into the Y= window as functions.

Use TABLE to show that for x-values other than zero, replacement values do NOT yield the same results in the two expressions.


3. Use the graphing calculator to solve the equation .
Enter each side of the equation as a function in Y= window and GRAPH

Use CALC, intersect to find the point where the graphs intersect.

Solving graphically, we see that x = 4 is the solution. Check by solving algebraically.

4. Find the zeros of the function .
Enter the function in Y= window and GRAPH.

Use CALC,zero to find the zeros of the function.

Notice that we have to enter a Left Bound and a Right Bound by moving the cursor appropriately.
Then press ENTER when given the Guess? screen and one of the zeros is given as shown below.


Using same steps, find the other zeros of the function.

5. Calculate .
Change MODE to a+bi setting and enter the calculation as follows. (Note: i is located above the period).

Notice the different appearance of the negative sign and the subtraction sign.

6. Solve .
Enter the sides of the inequality into the Y= window. To enter the absolute value, go to MATH under the NUM heading to enter abs, then enter the expression enclosed in a parenthesis.

GRAPH and find the x-coordinates at the points of intersection..

Hopefully, students can see from the screen that the graph of the absolute value is less than or equal to the graph of the horizontal line when .

TOP