What Does Odds Of Evens Or Greater Mean

Odd definition, differing in nature from what is ordinary, usual, or expected: an odd choice.

If there’s a positive sign next to the odds, that indicates the amount of money you would win if you bet $100. If the odds on a tennis player said +150, that means that for a $100 bet, you would. A 200 percent relative risk means that you are three times as likely to develop that condition. Risk seems greater when put in these terms. A 100 percent increase in risk may seem enormous, but if the risk began as 1 in 100 people, a 100 percent increase in risk means that 2 out of 100 will be affected.

They are special types of functions

Even Functions

A function is 'even' when:

What Does Odds Of Evens Or Greater Meaningful

f(x) = f(−x) for all x

In other words there is symmetry about the y-axis (like a reflection):

This is the curve f(x) = x2+1

They got called 'even' functions because the functions x2, x4, x6, x8, etc behave like that, but there are other functions that behave like that too, such as cos(x):


Cosine function: f(x) = cos(x)
It is an even function

But an even exponent does not always make an even function, for example (x+1)2 is not an even function.

Odd Functions

A function is 'odd' when:

−f(x) = f(−x) for all x

Note the minus in front of f(x): −f(x).

And we get origin symmetry:

This is the curve f(x) = x3−x

They got called 'odd' because the functions x, x3, x5, x7, etc behave like that, but there are other functions that behave like that, too, such as sin(x):


Sine function: f(x) = sin(x)
It is an odd function

But an odd exponent does not always make an odd function, for example x3+1 is not an odd function.

What does odds of evens or greater meaning

Neither Odd nor Even

Don't be misled by the names 'odd' and 'even' ... they are just names ... and a function does not have to be even or odd.

In fact most functions are neither odd nor even. For example, just adding 1 to the curve above gets this:

This is the curve f(x) = x3−x+1

It is not an odd function, and it is not an even function either.
It is neither odd nor even

Even or Odd?

Example: is f(x) = x/(x2−1) Even or Odd or neither?

Let's see what happens when we substitute −x:

=−x/(x2−1)

So f(−x) = −f(x) , which makes it an Odd Function

Even and Odd

The only function that is even and odd is f(x) = 0

What Does Odds Of Evens Or Greater Mean

Special Properties

Adding:

What Does Odds Of Evens Or Greater Meaning

  • The sum of two even functions is even
  • The sum of two odd functions is odd
  • The sum of an even and odd function is neither even nor odd (unless one function is zero).

Multiplying:

Evens Or Odds

  • The product of two even functions is an even function.
  • The product of two odd functions is an even function.
  • The product of an even function and an odd function is an odd function.