Please Help me with this question (Function/Graph)

H

Hostile

New member
Joined
Jul 8, 2022
Messages
1
Find an example of a function that produces the same image when its graph is reflected in the y-axis as it does when its graph is reflected in the x-axis. Graph the equation and the two images
 
Hostile said:
Find an example of a function that produces the same image when its graph is reflected in the y-axis as it does when its graph is reflected in the x-axis. Graph the equation and the two images
Click to expand...
Can you think of a function statement where exchanging 'x' with 'y' (and vice versa) will not change the graph?

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:


Please share your work/thoughts about this problem
 
Hostile said:
Find an example of a function that produces the same image when its graph is reflected in the y-axis as it does when its graph is reflected in the x-axis. Graph the equation and the two images
Click to expand...
You might imagine doing the two transformations, one after the other: reflect a graph in the y-axis, and then reflect the result in the x-axis. Do you see that if this returns the graph to the original, it will also satisfy the problem?

What kind of symmetry does this represent?

In any case, tell us your own thinking; that's how this site works, rather than doing all the thinking for you.
 
I don't think that anything would be a function except other than the function that contains just (0,0)
 
Last edited:
If it does not be to be a function, then draw anything in quadrant 1 (and I really mean anything). Then reflect that across the y-axis. Then reflect the whole graph across the x-axis.
Now look at this graph and think what might work.
 
Steven G said:
I don't think that anything would be a function except other than the function that contains just (0,0)
Click to expand...
Why would you say that? There are many functions that work. I think you may be misreading something.
Steven G said:
If it does not [have] to be a function, then draw anything in quadrant 1 (and I really mean anything). Then reflect that across the y-axis. Then reflect the whole graph across the x-axis.
Now look at this graph and think what might work.
Click to expand...
But you should draw a function, since that's what they ask for, and it doesn't have to be only in the first quadrant. (I recommend just keeping x>0.) And this exercise will then result in a function that works, though one might not immediately see the key idea I hinted at, about symmetry.

@Hostile, the main point is that you need to try something in order to understand the problem. Just pick any graph (again, I recommend drawing it only for positive x) and do what they say to it, to see what happens.
 
Hostile said:
Find an example of a function that produces the same image when its graph is reflected in the y-axis as it does when its graph is reflected in the x-axis. Graph the equation and the two images
Click to expand...
Subhotosh Khan said:
Can you think of a function statement where exchanging 'x' with 'y' (and vice versa) will not change the graph?
Click to expand...
Subhotosh Khan said:
xy = Constant ....... it is a rectangular hyperbola.
Click to expand...
I think you may be misreading the problem, though this is a valid answer. It is not about exchanging x and y (reflecting in y=x), but about reflecting in both x and y axes.
The answer is: Any odd function.
 
Dr.Peterson said:
I think you may be misreading the problem, though this is a valid answer. It is not about exchanging x and y (reflecting in y=x), but about reflecting in both x and y axes.
The answer is: Any odd function.
Click to expand...
Yes ... I surely did. Once my mind got trapped in f(x*y) as solution, there was no escape.
 
You must log in or register to reply here.
Top