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

1 Answer
mason m
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.

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