if you have anything on the screen you can clear it by pressing: CLEAR

Transcription

1 Graphing Calculators are really very powerful hand held computing devices. The allow mathematics problems to be investigated by those whose learning styles range from the symbolic to the visual to the numerical. When you turn the calculator on it will take you to the HOME Screen: This is the main sandbox that you will do your numerical work in when clear it should look like this: it by pressing: CLEAR if you have anything on the screen you can clear Your settings are found by pressing the MODE key: For the most basic operations they should be set all the way to the left:

2 You navigate around the screens by using the ARROW keys and you activate a command by moving over it and pressing ENTER Any menu that has numerical entries can also be activated by pressing the number associated with that Item Example: if you wanted to use the INTERSECT option in the CALC menu: You would press 2 nd - TRACE (the CALC key is located over the TRACE) And you would see this screen: you can then use the arrow keys to go down to intersect: and then press ENTER the first screen. or you could have just pressed the number 5 at WE WILL GO THROUGH THE INTERSECTION OF TWO FUNCTIONS LATER IN THE PACKAGE: CALCULATING: The benefit of a graphing calculator is the MULTI LINE display. You can follow what you are doing and what you have done: For instance if you want to take 6% tax on a $130 bill and find the total price: You would convert the 6% to a decimal by dividing by 100 You would then multiply that answer by the $ You would then add that answer back to the $

3 This screen shows that you can follow what you have done. The calcluator makes it even clearer: Putting the INPUT on the left and the OUTPUT on the right It allows for the teacher and student to follow a series of steps online and makes finding mistakes easier: Will it calculate fractions? YES but it does it by changing everything to decimals and then you have to ask it to convert it back: Example: Add 2/3 + 5/7 NOTE TWO THINGS HERE: 1. Fractions should always be entered in (PARENTHESES) for safety 2. You can see both the decimal answer and the fraction answer on the same screen. USER TIPS: The ANSWER key is found by pressing 2 nd then ( - ) {see yellow ANS} The fraction conversion key is found as the FIRST ITEM on MATH key 3

4 The ANSWER key automatically keeps the very last calculation done so you can reuse it without having to retype it in. You can use the Frac Key to reduce fractions as well. For instance, if you input 124/36 Frac it will return the reduced fraction to you or if you d rather see it as a decimal first, you can show both before it reduces: Directly to Fraction Decimal First, Then Fraction You can also recall either an answer to use by pressing 2 nd then ( - ) or you can bring back the last entry to edit it, pressing 2 nd then ENTER Where you can move around the entry using the arrow keys and deleting or inserting what you d like to change: Enter and Press 2 nd ( -) Press 2 nd Enter Move using Press ENTER to Execute To use that To make an Left arrow to Execute new Expression Result Edit change 4 to 14 Entry value GRAPHING: The top row of the keyboard is where you deal with the graphing functions Y= is where you put the function or functions to be graphed WINDOW is where you tell the machine where you want to look ZOOM is where you go to move closer in to part of the graph or where you go to back away and take a larger view 4

5 TRACE is how you can look at values along the graph GRAPH is how you tell the machine that you want to see the picture drawn for you when you have finished setting it up 2 First we ll Graph and manipulate y = ( x 2) 3 Input the Check the A shortcut Press Press Function Window to the standard Graph Trace Window If you press the arrows the cursor will move along the graph to the right (right arrow) or the the left (left arrow) and you will see the current value of both the input (x-value) and output (y-value) of the function at the same time: Moving to the left Moving to the right 5

6 User note: The values displayed have to do with the way the window is configured. The calculator is 94 dots wide by 63 dots up and XMax XMin down. So the trace values are spaced by taking in this ( 10) case we have = So, if we want the values to be nice we have to have a window is nicely divisible by 94. ZOOMING: Zooming allows us to get closer or to back away, it also allows us to trick the graph to have nice trace values Example: if we go to the ZOOM window, and go down to #4 DECIMAL and press enter we will get the following picture: Looks Different huh? Not really it s just a different viewing angle The window is now 9.4/94 or =.1 so each trace will be 1/10 th apart and the y-values will be those plugged in. Nice friendly values. We can also use the zoom to get a better look at a particular part of the graph. We can localize the region by drawing a box around the part we want to blow up. Let s go back to the original picture (ZOOM 6) and box off the part around the Y-Axis You use Zoom-Box by setting your first corner, pressing ENTER then dragging the box until you have covered the region you want to see. [If you make a mistake, or don t like what you see no worries just press GRAPH and start over] 6

7 Press Zoom Set first Corner Set opposite Press enter corner,enter New Graph New Window USER TIP: Zoom Memory Zprevious will back you up ONE SCREEN ONLY PRESS ENTER Back SOLVING EQUATIONS: The best way to understand what is going on when you solve equations is to look at the intersection of the two graphs since what you are really doing is finding the points where both functions exist at the same time. For instance if you wanted to find the solution to: 3x +5 = -2x 4 what you would really be doing is finding out where the line y=3x+5 intersects the line y = -2x 4 so, we ll put the left side of the equation in Y1 and the right side of the equation in Y2 and find the intersection. NOTE: We will do it in the following steps: 1. put 3x+5 in Y1 2. put 2x 4 in Y2 3. Press Zoom-6 to make sure we see where they meet (very important step) 4. Press 2 nd Trace 5 (intersection) to start the process 5. Move the cursor close to the point where they meet (it does NOT have to be on it, just close) 6. Press Enter 3 Times. 7

8 The solution to the equation then is X = -1.8 USER TIP: You can frequently convert that to a fraction by going immediately back to the home screen { Press 2 nd Mode (Quit)} and pressing X Frac. This will work well for linear equations it will NOT work well for other types If there are two solutions you can find them one at a time: Example: 2 Solve for X: x x 6= 2x 3 The screens above show the results of both intersections. NOTE: these are irrational results and trying to change them to fractions does not work: See: No Fractions 8

9 Using the TABLE Feature: Sometimes you want to take a look at many values of a function you can do that using the TABLE feature: HOWEVER, before you sit at the table you must SET the Table. You find those utensils in the drawer marked :TBLSET (press 2 nd WINDOW) at this point. NOTE: You may NOT have the same values TblStart: This is the first value you will SEE at the beginning of the table* *(you can scroll the table either way this just a convenient start point) Tbl: This is the increment between table value inputs Indpnt: You have your choice of the table filling in automatically or waiting for you to ask for the next X value Depend: You have your choice of the table filling in automatically or waiting for you to ask for the next Y value Example: 2 Let s create a table of values for the function: y = x x Put the function in Y1 2. Go to TblSet and start the table at 0, with an increment of 1 3. Call up the table on screen [press 2 nd Graph] 9

10 If you go up and highlight the Y1 it will tell you what the formula is also: If you leave the cursor on the X table you can scroll the values both ways and see the resultant Y values DID YOU NOTICE YOU CAN SEE THE VALUE OF THE ROOTS FROM THE TABLE IN THIS CASE? When X=4, Y=0 and When X=-3, Y=0 10