How do you know if y = 1/x is an even or odd function?

1 Answer
Dec 21, 2015

Odd

Explanation:

Call the function

f(x)=1/x

Now,

f(x) is even if f(-x)=f(x).

f(x) is odd if f(-x)=-f(x).

Find f(-x):

f(-x)=1/(-x)=-1/x

Since -1/x=-f(x), the function is odd.

graph{1/x [-9.295, 10.705, -4.48, 5.52]}

A special feature of odd functions is that they have "origin symmetry." This means that they can be reflected over the point (0,0) and look identical.