How do you determine if #f(x)=-sinx# is an even or odd function?
1 Answer
Oct 8, 2016
f(x) is an odd function.
Explanation:
To determine if f(x) is even/odd consider the following.
• If f(x) = f( -x) then f(x) is even ,
#AAx" in the domain"# Even functions are symmetrical about the y-axis.
• If f( -x) = - f(x) then f(x) is odd,
#AAx" in the domain"# Odd functions have half-turn symmetry about the origin.
Test for even
#f(-x)=-sin(-x)=-(-sinx)=sinx# Since f(x) ≠ f( -x) then f(x) is not even.
Test for odd
#-f(x)=-(-sinx)=sinx# Since f( -x) = - f(x) then f(x) is odd.
graph{-sinx [-10, 10, -5, 5]}
