# Thread: Summer work confusing... help by tomorrow?

1. ## Summer work confusing... help by tomorrow?

On my summer work I have to give explination for statements

These are the only 3 I don't get:

1.if (x,y)is a point on the graph of f(x) then (-x, y) is also a point on the graph
2.if (x,y)is a point on the graph of f(x) then (x, -y) is also a point on the graph
3.if (x,y)is a point on the graph of f(x) then (-x, -y) is also a point on the graph

I searched everywhere, for the first two I found something about symmetry but I still don't really get what the statement means, I found nothing on the last one

2. ## Re: Summer work confusing... help by tomorrow?

There has to be more to the problem.

1) isn't in general true. Consider $y=x$

2) isn't in general true. Consider $y = x^2$

3) isn't in general true. Again consider $y=x^2$

3. ## Re: Summer work confusing... help by tomorrow?

Originally Posted by Sar34
On my summer work I have to give explination for statements

These are the only 3 I don't get:

1.if (x,y)is a point on the graph of f(x) then (-x, y) is also a point on the graph
2.if (x,y)is a point on the graph of f(x) then (x, -y) is also a point on the graph
3.if (x,y)is a point on the graph of f(x) then (-x, -y) is also a point on the graph

I searched everywhere, for the first two I found something about symmetry but I still don't really get what the statement means, I found nothing on the last one
What graph are you talking about? That's important! What is true for one graph may not be true for another.

4. ## Re: Summer work confusing... help by tomorrow?

Originally Posted by Sar34
On my summer work I have to give explination for statements

These are the only 3 I don't get:

1.if (x,y)is a point on the graph of f(x) then (-x, y) is also a point on the graph
2.if (x,y)is a point on the graph of f(x) then (x, -y) is also a point on the graph
3.if (x,y)is a point on the graph of f(x) then (-x, -y) is also a point on the graph

I searched everywhere, for the first two I found something about symmetry but I still don't really get what the statement means, I found nothing on the last one
These are indeed about symmetry. For example, consider the first one. For any point $(x,y)$, the point $(-x,y)$ is its reflection in the y axis. That says for each point on the graph, its mirror image in the $y$ axis is also on the graph. Look at the graph of $y = x^2$. Do you see that the right side of the graph is the reflection of the left side of the graph in the $y$ axis? So any graph that has property 1 has that kind of symmetry, called symmetry about the $y$ axis.

Once you understand that, you should be able to put into words what graphs satisfying 2. or 3. look like. They are also about symmetry.