- #1
eax
- 61
- 0
Is this right?
An even function has this property
f(x)=f(-x)
and an odd function has this property
-f(x) = f(-x)
An even function has this property
f(x)=f(-x)
and an odd function has this property
-f(x) = f(-x)
hypermorphism said:Yes. Note that many functions are neither even nor odd.
eax said:Thanks! I just had a test, and one question said to give an example of an odd function and another to prove a function is odd. I looked at the "prove" question and guessed correctly :).
An even function is a mathematical function where the output remains unchanged when the input is replaced with its negative value. In other words, f(x) = f(-x) for every x in the function's domain. This results in a graph that is symmetric about the y-axis.
An odd function is a mathematical function where the output changes sign when the input is replaced with its negative value. In other words, f(x) = -f(-x) for every x in the function's domain. This results in a graph that is symmetric about the origin.
To determine if a function is even or odd, you can use the symmetry test. If the function passes the symmetry test, it is even. If the function fails the symmetry test, it may be odd, but further testing is needed to confirm. Additionally, you can also check the function algebraically by plugging in -x for x and seeing if the output remains unchanged or changes sign.
No, a function cannot be both even and odd. A function can only have one type of symmetry - either even or odd. However, a function can have neither symmetry and be considered neither even nor odd.
Some examples of even functions include f(x) = x², f(x) = cos(x), and f(x) = |x|. Some examples of odd functions include f(x) = x³, f(x) = sin(x), and f(x) = √x. It is important to note that not all functions will fall into the categories of even or odd, as they may have neither symmetry.