# Summer work confusing... help by tomorrow?

• Sep 5th 2018, 08:38 PM
Sar34
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
• Sep 5th 2018, 08:45 PM
romsek
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\$
• Sep 6th 2018, 05:21 AM
HallsofIvy
Re: Summer work confusing... help by tomorrow?
Quote:

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.
• Sep 6th 2018, 08:41 PM
Walagaster
Re: Summer work confusing... help by tomorrow?
Quote:

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.