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:
- Graph your equation by typing the equation into a
y= slot.
- Go to
TABLE SETUP screen (by pressing [2nd][TBLSET].)
- Make sure that your independent variable (
x) is set to Ask.
- Then go to the
TABLE screen (by pressing [TABLE] button.)
- 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.
More information about Even and Odd functions on Wikipedia.
Complex numbers are not supported—on simultaneous equations or on matrices—on the fx-115es plus scientific calculator.
Indeed, no scientific calculator (neither T.I., Sharp or Casio) supports these two kinds of problem solving in CPLX mode.
For that, you will need to choose a graphing calculator with a CAS (Computer Algebra System).
/Silicon Valley Regards
Best Answer
I'm still not sure what happened, but I deleted the values in $Y_1$ and $Y_2$ for the umpteenth time, and suddenly everything worked fine.