You seem to have the right idea, but a few values never will be sufficient. You must prove generally that f(x) = -f(-x).
Reading on how to check for symmetry, book uses this equation . I am asked to do the same but with this equation;
I want to know if I did right or done something wrong...
In looking for points to plot I did the following:
X___Y
0___0
1___-5
2___-10
-1___5
-2___10
Now, about checking these points for symmetry. If I was to check for the y Axis I would have to replace x by -x, so then the equation would look like this;
correct?
So my Y axis ends up being positive = right?
And if checking for the x Axis I would replace y by -y,
so now my y axis remains a negative thus giving me this;
= so far correct?
So for this equation y=-5x, we can say that it is only symmetric with respect to the origin, yes?!
Thanks for taking the time on this!
There are two different types of symmetries which could be checked very easily. (There are others which are a lot more difficult to handle):
1. Symmetry about the y-axis.
If the graph of a function is symmetric about the y-axis all x-values from the domain of the function has to satisfy the equation:
With your example:
. So you know that the graph of this function is not symmetric to the y-axis.
2. Symmetrie about the origin.
If the graph of a function is symmetric about the origin all x-values from the domain of the function has to satisfy the equation:
With your example:
. So you know that the graph of this function is symmetric to the origin.
Yes, you are right!
I mean always. DISproof requires only one counter example. It is of no consequence if you can show 6,423,010 examples. To prove that something is ALWAYS the case, you cannot do it unless you can demonstrate it for EVERY case. That is a tall order for all Real Numbers unless you can establish a continuous relationship.