Symmetry in Graphs: Conditions & Possibilities

In summary, for a graph of any function, one of the conditions for symmetry must exist: either symmetry about the y-axis, x-axis, or origin. However, it is possible for a curve to pass through the two points highlighted by one of these conditions without appearing symmetric.
  • #1
Danish_Khatri
26
0
For a graph of any function, one of following conditions is said to exist so as for it to be symmetric:
a graph is symmetric about y-axis if along with a point (x,y) a point (-x, y) exists.
a graph is symmetric about x-axis if along with a point (x,y) a point (x, -y) exists.
a graph is symmetric about origin if along with a point (x,y) a point (-x, -y) exists.
isn't it possible that one of the above condition is satisfied but still the graph is not symmetric. what i want to say is that can't it be possible for a curve to have such shape that it does not look symmetric but still passes through the two points highlighted by one of the conditions mentioned above?
 
Physics news on Phys.org
  • #2
Welcome to PF!

Hi Danish_Khatri! Welcome to PF! :wink:
Danish_Khatri said:
For a graph of any function, one of following conditions is said to exist so as for it to be symmetric:
a graph is symmetric about y-axis if along with a point (x,y) a point (-x, y) exists.
a graph is symmetric about x-axis if along with a point (x,y) a point (x, -y) exists.
a graph is symmetric about origin if along with a point (x,y) a point (-x, -y) exists.
isn't it possible that one of the above condition is satisfied but still the graph is not symmetric. what i want to say is that can't it be possible for a curve to have such shape that it does not look symmetric but still passes through the two points highlighted by one of the conditions mentioned above?

I think it means for every (x,y) on the curve … :smile:
 
  • #3
Thanks for your help dear... :-)
 

1. What is symmetry in graphs?

Symmetry in graphs refers to the balance and proportionality of a graph's elements. It is the property of a graph in which one half is a mirror image of the other half when folded along a specific line or axis.

2. What are the conditions for a graph to have symmetry?

In order for a graph to have symmetry, it must have a line or axis of symmetry that divides the graph into two equal and identical halves. The graph must also have at least one point on the line of symmetry that remains unchanged when reflected.

3. What are the types of symmetry in graphs?

There are three types of symmetry in graphs: reflectional symmetry, rotational symmetry, and point symmetry. Reflectional symmetry is when a graph can be folded along a line to create two identical halves. Rotational symmetry is when a graph can be rotated around a central point and still look the same. Point symmetry is when a graph can be reflected across a point to create two identical halves.

4. Can all graphs have symmetry?

No, not all graphs have symmetry. Some graphs may have partial symmetry or no symmetry at all. It depends on the shape and arrangement of the elements in the graph.

5. How is symmetry in graphs useful in real-world applications?

Symmetry in graphs is useful in many real-world applications, such as architecture, design, and engineering. It helps in creating visually appealing and balanced structures. It also plays a role in understanding patterns and relationships in data analysis and can aid in problem-solving and decision-making processes.

Similar threads

I Inverse Functions: x=f(y) and X=f^-1(y)
    • Calculus
Replies
4
Views
1K
B Why is this definite integral a single number?
    • Calculus
Replies
20
Views
2K
I Open interval or Closed interval in defining convex function
    • Calculus
Replies
4
Views
2K
B Linearization of a function error viewed with differentials
    • Calculus
Replies
14
Views
1K
B Tangents to a curve as functions of different variables
    • Calculus
Replies
5
Views
1K
A few questions to make sure I understand Fourier series
    • Calculus and Beyond Homework Help
Replies
3
Views
260
B Calculating shaded area: I'm getting discrepancies between methods
    • Calculus
Replies
3
Views
302
I The Basic Area Problem (introduction to the topic of integrals)
    • Calculus
Replies
24
Views
2K
I How to evaluate the enclosed area of this implicit curve?
    • Calculus
Replies
2
Views
2K
I How to find the maximum arc length of this equation?
    • Calculus
Replies
3
Views
1K

Hot Threads

Recent Insights

Back
Top