How do you determine if #f(x) = x - absx# is an even or odd function?

1 Answer
Oct 22, 2016

An even function is a function where #f(-x)=f(x)# and an odd function is a function where #f(-x)=-f(x)#

Explanation:

Take a look at this #cos# graph:
graph{cos(x) [-10, 10, -5, 5]}
As you can see, the #y#-value for #pi/2# is the same as the #y#-value for #-pi/2#, so it's an even function.

Now look at this #sin# graph:
graph{sin(x) [-10, 10, -5, 5]}

The #y#-value for #pi/2# is #1# whilst the #y#-value for #-pi/2# is #-1#, so it's an odd function.