Can function be even and odd?

Can function be even and odd?

Note: A function can be neither even nor odd if it does not exhibit either symmetry. For example, f(x)=2x f ( x ) = 2 x is neither even nor odd. Also, the only function that is both even and odd is the constant function f(x)=0 f ( x ) = 0 .

Can a function be both even and odd give reason for your answer?

Odd functions have graphs that are symmetric with respect to origin. Even functions have graphs that are symmetric with respect to y-axis. So, graph of f(x)=0 satisfies both conditions, therefore it is both odd and even.

Can a function be both even and odd Can you describe all such functions?

Both Even and Odd Functions – A real-valued function f(x) is said to be both even and odd if it satisifies f(-x) = f(x) and f(-x) = -f(x) for all values of x in the domain of the function f(x). There is only one function which is both even and odd and that is the zero function, f(x) = 0 for all x.

What is not even and odd function?

Answer: If f(x) = – f(-x), then f is an odd function. If f(x) = f(-x), then f is an even function. If neither of these conditions hold, then f is neither even nor odd function. Let use the definition of even and odd function to answer this question.

What is both an odd and even number?

Zero is the only number that is both odd and even. Zero has many special qualities. It is neither negative nor positive. Any number multiplied by zero is equal to zero.

Is a rational function even or odd?

Even and odd rational functions (MathsCasts) – YouTube

Is zero a odd or even function?

When 0 is divided by 2, the resulting quotient turns out to also be 0—an integer, thereby classifying it as an even number. Though many are quick to denounce zero as not a number at all, some quick arithmetic clears up the confusion surrounding the number, an even number at that.

How do you tell if a function is even or odd from a table?

Even functions are symmetrical about the y-axis: f(x)=f(-x). Odd functions are symmetrical about the x- and y-axis: f(x)=-f(-x).

What are the properties of even and odd function?

The product of two even functions is even, and the product of two odd functions is even. The product of an even function and an odd function is an odd function. The quotient of two even functions is even, and the quotient of two odd functions is even.

Is a linear function even or odd?

Use their function graphs to determine whether they are even, odd, or neither. This linear function is symmetric about the origin and is an odd function: f ( x ) = f ( − x ) . As shown earlier in the concept, this quadratic function is symmetric about the -axis and is an even function: f ( x ) = f ( − x ) .

Can a number be both even and prime?

The number 2 is prime. (It is the only even prime.)

Is one number even or odd?

One is the first odd positive number. Some examples of odd numbers are 1, 3, 5, 7, 9, and 11. An integer that is not an odd number is an even number.

Are linear functions even or odd?

How do you tell if a function is neither even or odd?

If f(x) ≠ f(−x) and −f(x) ≠ f(−x) for some values of x, then f is neither even nor odd.

Is a identity function even or odd?

The square function is even, and the identity function is odd.

What is mean by even function and odd function?

Here, the function f(x) is called an even function when we substitute -x in the place of x and get the expression the same as the original function. That means, the function f(x) is called an even function if f(-x) = x for all real values of x. Even function: f(-x) = f(x) Odd function: f(-x) = -f(x)

Is identity function even or odd?

What is the number that is both even and odd?

Zero

Zero is the only number that is both odd and even. Zero has many special qualities. It is neither negative nor positive. Any number multiplied by zero is equal to zero.

Is 0 an odd or even number?

So what is it – odd, even or neither? For mathematicians the answer is easy: zero is an even number.

Is zero function odd or even?

Is 0 an Even Number? The answer is easy: Yes, zero is an even number. Usually, zero together with the even numbers, so certainly it is not an odd number. An even number is formally defined as an integer of the form n = 2x, where x is an integer.

Are quadratic functions even or odd?

Answer and Explanation:
A parabola can either be even or it can be neither even nor odd, but it cannot be odd. In general, a parabola is the graph of a quadratic function of the form f(x) = ax2 + bx + c.

What is odd and even function with one example?

Example. The polynomial function f(x)=x2+x4+x6 is even. The polynomial function f(x)=x+x3+x5 is odd. The polynomial function f(x)=1+x+x2 is neither odd nor even.

Is linear function even or odd?

[Figure 4]
This linear function is symmetric about the origin and is an odd function: f ( x ) = f ( − x ) . As shown earlier in the concept, this quadratic function is symmetric about the -axis and is an even function: f ( x ) = f ( − x ) .

Can an integer be even and odd?

Every integer is either even or odd, and no integer is both even and odd. This includes 0, which is even. Figure out whether 1729 is an odd or even number. Since the remainder obtained on dividing 1729 by 2 is 1, 1729 is an odd number.

Is infinity even or odd?

I explained that infinity is neither even nor odd. It’s not a number in the usual sense, and it doesn’t obey the rules of arithmetic. All sorts of contradictions would follow if it did. For instance, “if infinity were odd, 2 times infinity would be even.