Question

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

Answer 1

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]}