Reflection about the y-axis.
It is an odd function. Even functions use the y-axis like a mirror, and odd functions have half-circle rotational symmetry.
Bilateral symmetry.
It is an increasing odd function.
Bilateral symmetry
Bilateral symmetry
An even function is a function that creates symmetry across the y-axis. An odd function is a function that creates origin symmetry.
It is an odd function. Even functions use the y-axis like a mirror, and odd functions have half-circle rotational symmetry.
You can tell if a function is even or odd by looking at its graph. If a function has rotational symmetry about the origin (meaning it can be rotated 180 degrees about the origin and remain the same function) it is an odd function. f(-x)=-f(x) An example of an odd function is the parent sine function: y=sinx If a function has symmetry about the y-axis (meaning it can be reflected across the y-axis to produce the same image) it is an even function. f(x)=f(-x) An example of an even function is the parent quadratic function: y=x2
You can tell if a function is even or odd by looking at its graph. If a function has rotational symmetry about the origin (meaning it can be rotated 180 degrees about the origin and remain the same function) it is an odd function. f(-x)=-f(x) An example of an odd function is the parent sine function: y=sinx If a function has symmetry about the y-axis (meaning it can be reflected across the y-axis to produce the same image) it is an even function. f(x)=f(-x) An example of an even function is the parent quadratic function: y=x2
A function f(x) is even if f(-x) = f(x). A graph of f(x) would be symmetric about the y-axis (vertical symmetry about x=0). f(x) need not be "well-behaved" or even continuous, unlike the examples given in Wikipedia article on "Even and odd functions". The article does make this clear - under "Some facts".
Symmetry in a function significantly simplifies its Fourier series representation. For even functions, only cosine terms are present, while odd functions contain only sine terms. This reduces the number of coefficients that need to be calculated, leading to a more straightforward analysis of the function's periodic behavior. Additionally, symmetry can enhance convergence properties, allowing for faster and more efficient approximations of the function.
Lateral Symmetry.
Bilateral symmetry
bilateral symmetry
Bilateral symmetry.
Radial Symmetry
turn symmetry