1. ## Checking for symmetry

Reading on how to check for symmetry, book uses this equation $\displaystyle y=x^3$. I am asked to do the same but with this equation;
$\displaystyle y=-5x$

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;

$\displaystyle y=-5-x$ correct?

So my Y axis ends up being positive $\displaystyle y=-5(-1)$ = $\displaystyle y=5$ right?

And if checking for the x Axis I would replace y by -y, $\displaystyle -y=-5x$

so now my y axis remains a negative thus giving me this;

$\displaystyle -y=-5(1)$ = $\displaystyle y=-5$ 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!

2. You seem to have the right idea, but a few values never will be sufficient. You must prove generally that f(x) = -f(-x).

$\displaystyle f(x) = x^{3}$

$\displaystyle -f(-x) = -(-x)^{3} = x^{3} = f(x)$

3. Originally Posted by TKHunny
You seem to have the right idea, abut a few values never will be sufficient. You must prove generally that f(x) = -f(-x).

$\displaystyle f(x) = x^{3}$

$\displaystyle -f(-x) = -(-x)^{3} = x^{3} = f(x)$
... sorry, when you say "will never be sufficient", you mean once graphed? And how does f(x) work into y=-5x?

many thanks again!

4. Originally Posted by Morzilla
Reading on how to check for symmetry, book uses this equation $\displaystyle y=x^3$. I am asked to do the same but with this equation;
$\displaystyle y=-5x$

I want to know if I did right or done something wrong...

...
There are two different types of symmetries which could be checked very easily. (There are others which are a lot more difficult to handle):

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:

$\displaystyle f(x) = f(-x)$

$\displaystyle -5x\ {\buildrel \rm ? \over =}\ -5(-x)~\implies~-5x \ne 5x$ . So you know that the graph of this function is not symmetric to the y-axis.

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:

$\displaystyle f(x) = -f(-x)$

$\displaystyle -5x\ {\buildrel \rm ? \over =}\ -\left( -5(-x)\right)~\implies~-5x = -5x$ . So you know that the graph of this function is symmetric to the origin.