# Checking for symmetry in a graph on the TI-84 Plus

I was using the TI-84 Plus calculator to check for Y-Axis symmetry in the graph of "cos(2X+1)" and as I had to do it fast (I was in the middle of a test), I quickly noted that it was symmetrical. I had set the zoom to "ZTrig". This is (exactly)what I saw :

But it turned out that the graph was not symmetrical. This is the graph by Google Graphs.

How do I identify correctly if a graph is symmetrical about an axis(Mostly the Y-axis) or not in the TI-84 Plus

Update 1 :

@Summea, This is what I got when I used the table method. This works fine, but is there a way to get the accuracy more than 5 digits as some problems may require it?

@Amzoti, I set the window variables like this (I changed the "Xscl" to 180, from 90, to see if it zooms in, but for some reason, the graph remains the same.

The small bars on the graph which indicate the points have really moved, but the graph remains the same.

I also tried another method, i.e. using the "ZBox" function to select a box and zoom in there. This is what I saw:

The graph hardly shows any difference, even now. How can I solve this?

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It would seem that this might be an issue with trying to look at a global - like behavior on a very small screen and that it loses resolution and detail as a result. Is there a better way to zoom to see this on any limited size screen? I suppose you could have looked the the pieces of the graph in more detail, but this takes time. For example, look at WA and see how it shows two levels of details. Regards –  Amzoti Apr 18 '13 at 3:56
Thanks, @Hele! ;-) –  amWhy Apr 30 '13 at 2:56

One way you could check for symmetry on the calculator is to check if the function being graphed is even or odd.

On the calculator:

1. Graph your equation by typing the equation into a y= slot.
2. Go to TABLE SETUP screen (by pressing [2nd][TBLSET].)
3. Make sure that your independent variable (x) is set to Ask.
4. Then go to the TABLE screen (by pressing [TABLE] button.)
5. From there, you could try typing some values into the x column (for example, some "mirrored numbers" such as: -4,-2,-1,1,2,4) to see if there are any patterns going on with the y values for each (negative) and (positive) "pair" of numbers.

## Even Functions

If the y values for each corresponding (negative) and (positive) x are equal to each other, we can know that the graph is even and is symmetrical with respect to the y-axis.

Example: $y=x^2$

 x  | y
-4  | 16
-2  | 4
-1  | 1
1  | 1
2  | 4
4  | 16


(See how the y values "match up" with each other?)

## Odd Functions

If the y values for each corresponding (negative) and (positive) x are the exact opposite of each other (for example, -1 and 1) we can know that the graph is odd and is symmetrical about the point of origin. (Sort of like a "diagonal symmetry".)

Example: $2x^3-4x$

 x  |  y
-4  | -112
-2  | -8
-1  |  2
1  | -2
2  |  8
4  |  112


(Notice how the y values "match up" with each other, but in this case, the y values are the exact opposite of each other with respect to the real number line.)

Or in other words, if you took half of the graphed odd function's line (starting at the point of origin... which might be something like (0,0) on the graph,) and rotated the line 180 degrees about the point of origin, the line you moved would look the same as the line you didn't move. (Meaning, the lines would perfectly overlap.)

And note, this is just one simple way to check for symmetry; there are probably cases where a more-detailed process needs to be used.

@Hele Great to hear :) Well, as far as getting more decimal values on your calculator, if you highlight the individual y1 values in your TABLE (like in the first picture of your update above,) does it show you a more detailed version of that y1 variable at the bottom of your calculator screen? –  summea Apr 24 '13 at 6:49