Graphing, Tracing, and Zooming

Example: Graph y=-2x+3

The Old fashioned way: Table of Values

 x y 0 3 1 1 -1 5 2 -1

Graph on a Cartesian Plane

The Modern Way: (with a graphing calculator)

What we will do:

Enter the function into the function list

Set the viewing window, if necessary

Graph it

How to do it:

1) Press the gray MENU key

2) Select the GRAPH icon using the arrows and the EXE blue key or pressing 4

3) Enter -2x+3 into Y1 (which should be selected)

4) To store it in memory press the EXE blue key

5) Since default viewing window is o.k., just graph it by pressing F4 (DRAW) .

Example: Do the same with another function, say y=x2-2x.

What we will do:

Enter the function into the function list

Set the viewing window, if necessary

Graph it

How to do it:

Since we are already in the GRAPH mode omit steps 1 and 2 above and

1) Press the G<->T key to see the function list (left of F1 key)

2) Enter x2-2x into Y2 (which should be selected)

3) To store it in memory press the EXE blue key

4) Since default viewing window is o.k., just graph it by pressing F4 (Draw).

Example: Graph a function in a different viewing window.

Graph y= -2x2 +6 in the default window. As you can see, this is not the best view for this function. Change the viewing window to Xmin=-3, max=3, scl=1, Ymin=-3, max=8, scl=1.

How to do it:

1) Press SHIFT F3 to get to the V-Window

2) Enter the appropriate values using the arrows and number keys:

 Xmin: -3 max: 3 scl: 1 Ymin: -3 max: 8 scl: 1

4) Draw it by pressing F4 (Draw).

Example: Tracing on y= -2x2 +6.

How to do it:

1) From the GRAPH Mode, press the G<->T (Graph<->Text) key (left of F1 key) until you see the graph.

2) Trace by pressing the F1 key (or SHIFT F1).

3) Using the left and right cursor keys,"walk" on the function.

Tracing can be used to approximate important values like the x and the y-intercepts. Recall that an x-intercept is the x value for which y=0. Recall that the y-intercept is the value of the function when x=0.

For this function, approximate the left x-intercept. Your approximation should make y as close to zero as possible, or as needed.

Example: Zooming lets you enlarge or reduce a graph on the graph display. Let’s zoom on y= -2x2 +6.

Zoom In enlarges a graph using the preset zoom factors entered into the calculator.

We may get a better approximation to the x-intercept in example 4 by "getting closer" to it, or "zooming in" on it.

1) Trace to the left x-intercept to approximate it (or to the place you want to be the center of the new graph). Remember to get the best approximation you can.

2) Get the Zoom functions by pressing F2. You should see now different options for the F1, F2, F3, and F4 keys. They are BOX, FACT, IN, and OUT respectively.

3) Since we want to get close to the x-intercept, press F3 (IN).

4) Repeat steps 1-3 as needed

Zoom Out reduces a graph using the preset zoom factors entered into the calculator. As practice, let’s zoom out on y= -2x2 +6.

1) Trace to the place you want to be the center of the new graph.

2) Get the Zoom functions by pressing F2. You should see now different options for the F1, F2, F3, and F4 keys. They are BOX, FACT, IN, and OUT respectively.

3) Press F4 (OUT).

Zoom ORIG. There is one more option within the ZOOM functions. It is hidden from us when we first press F2. To see it we must press the "MORE" key, the green arrow located to the right of F4. Pressing ZOOM (F2) and then the "MORE" key, we see the option ORIG in F1. Pressing the "MORE" key again brings you back to the other options. As you can imagine, ORIG brings you back to the viewing window of origin. Press Zoom ORIG (Zoom, "MORE", F1) now.

Zoom BOX enlarges the graph using a given viewing box. Let’s approximate the left x-intercept. After pressing Zoom ORIG the viewing window should be Xmin=-3, max=3, scl=1, Ymin=-3, max=8, scl=1. If it is not, enter these values in the viewing window. Then follow these instructions:

1) Press zoom and then F1 to select Zoom BOX.

2) Using the cursor keys move the pointer to the location of one of the corners of the box you want to draw.

3) Press EXE to specify the location of that corner.

4) Using the cursor keys move the pointer to the location of the corner that is diagonally across from the first corner.

5) Press EXE to specify the location of this corner. When you do this, the part of the graph inside the box is enlarged to fit the entire screen.

Zoom FACT allows you to set the desired zoom factors. If you would like to zoom in and enlarge the graph 5 times its original settings in both x and y change the zoom settings to Xfact: 5 and Yfact: 5. Similarly if you would like to reduce the graph 5 times its original settings.

For example, if the viewing window is set at Xmin: -1, max: 1, scl: 1, Ymin: -1, max: 1, scl: 1, and if the zooming factors are set at Xfact: 5 and Yfact: 5, after you zoom out from the origin, the new window will be at Xmin: -5, max: 5, scl: 1, Ymin: -5, max: 5, and scl: 1 (five times removed from the original perspective). If instead you zoom in with center the origin the new window will be Xmin: -.2, max: .2 scl: 1, Ymin: -.2, max: .2, and scl: 1 (five times closer from the original perspective). The calculator’s default zooming factor is 2 and it usually is very adequate.

1) Graph y=3x+5 on the following V-window: Xmin: -4, max: 1, scl: 1, Ymin: -2, max: 7, scl: 1. Using the TRACE and ZOOM routines, approximate the x-intercept for this function. Make sure you practice with the different zoom features.

2) Graph y=-3x2+2.5x on the default window. Using the TRACE and ZOOM functions, approximate the right x-intercept for this function. Make sure you practice with the different zoom features.