Can an odd function be periodic?

Examples of odd functions are t, t3,sint,sinnt. A periodic function which is odd is the saw-tooth wave in Figure 15. Some functions are neither even nor odd. The periodic saw-tooth wave of Figure 13 is an example; another is the exponential function et.

How do you know if a periodic function is odd or even?

The most easy and simplest way is that find f (-x) of the function f (x) and if f(-x)=f (x) then the function f (x) is an even and if f (-x)= -f (x) then the function f(x) is an odd function.

Do odd functions reflect over the X axis?

A function f(x) is even if f(-x) = f(x). The function is odd if f(-x) = -f(x). An even function has reflection symmetry about the y-axis. An odd function has rotational symmetry about the origin.

What is odd periodic function?

integration functions periodic-functions. Given an odd function f, defined everywhere, periodic with period 2, and integrable on every interval. Let g(x)=∫x0f(t)dt. I know that ∫b−bf(t)dt=0 for b∈R if it is odd function, and f(t)=f(t+2n) where n is integer if it is periodic with period 2.

What makes a function odd?

A function f is odd if the graph of f is symmetric with respect to the origin. Algebraically, f is odd if and only if f(-x) = -f(x) for all x in the domain of f.

Is it possible for a periodic function to be even?

A periodic function has a graph with a basic pattern that repeats at regular intervals. For example, sin x is periodic and its period is 2 pi. f(x) = f(x+a) = f(x+2a) = .. A function is said to be even if f(x) = f(-x) for all values of x.

What happens if you reflect an even function across the y-axis?

Even functions have graph symmetry across the y-axis, and if they are reflected, will give us the same function. Odd functions have 180 rotational graph symmetry, if they are rotated 180 about the origin we will get the same function.

Which of the following is odd function?

Example: x and sinx are odd functions. A function f(x) is an even function if f(-x) = f(x). Thus g(x) = x2 is an even function as g(x) = g(-x). So the function g(x) = 4x is an odd function.

What are odd and even functions in network theory?

In mathematics, even functions and odd functions are functions which satisfy particular symmetry relations, with respect to taking additive inverses. They are important in many areas of mathematical analysis, especially the theory of power series and Fourier series.

What is a period in a periodic function?

The time interval between two waves is known as a Period whereas a function that repeats its values at regular intervals or periods is known as a Periodic Function. In other words, a periodic function is a function that repeats its values after every particular interval.

Which of the following is not periodic function?

We know, √cosx and sin-1 both are periodic. So, this function is also periodic. As we can see, T is dependent on the value of x and hence, is not a constant. So cos(x2) is not periodic.

What is the rule of reflection over the y-axis?

The rule for a reflection over the y -axis is (x,y)→(−x,y) .