What is the symmetry of a function?

What is the symmetry of a function?

A symmetry of a function is a transformation that leaves the graph unchanged. Consider the functions f(x) = x2 and g(x) = |x| whose graphs are drawn below. Both graphs allow us to view the y-axis as a mirror. A reflection across the y-axis leaves the function unchanged. This reflection is an example of a symmetry.

How do you determine symmetry of a function?

Algebraically check for symmetry with respect to the x-axis, y axis, and the origin. For a function to be symmetrical about the origin, you must replace y with (-y) and x with (-x) and the resulting function must be equal to the original function.

How do you determine symmetry type?

Tests for Symmetry

1. A graph will have symmetry about the x -axis if we get an equivalent equation when all the y ‘s are replaced with –y .
2. A graph will have symmetry about the y -axis if we get an equivalent equation when all the x ‘s are replaced with –x .

How do you find the symmetry of a graph?

A graph is symmetric with respect to a line if reflecting the graph over that line leaves the graph unchanged. This line is called an axis of symmetry of the graph. A graph is symmetric with respect to the x-axis if whenever a point is on the graph the point is also on the graph.

What is symmetry in calculus?

2. Symmetry. The graph of an even function is symmetrical with respect to the axis y while the graph of an odd function is symmetric with respect to the origin. When a function is odd or even, we study the function in its interval of symmetry and complete by symmetry. Example: f(x) = 1/x is odd.

What is an example of symmetry?

Real-life examples of symmetry Reflection of trees in clear water and reflection of mountains in a lake. Wings of most butterflies are identical on the left and right sides. Some human faces are the same on the left and right side. People can also have a symmetrical mustache.

What are the different types of symmetry?

There are four types of symmetry that can be observed in various situations, they are:

• Translation Symmetry.
• Rotational Symmetry.
• Reflection Symmetry.
• Glide Symmetry.