Question

How do you determine if `f(x)= - 4 sin x` is an even or odd function?

Answer 1

`f(x)=-4sinx` is an odd function.

Explanation:

An odd function is one for which `f(-x)=-f(x)`. While for an even function `f(-x)=f(x)`.

As `f(x)=-4sinx`

`f(-x)=-4sin(-x)=-4×-sinx=4sinx=-f(x)`

Hence `f(x)=-4sinx` is an odd function.

Answer 2

odd function.

Explanation:

To determine if f(x) is even/odd consider the following.

• If f(x) = f( -x) , then f(x) is even

Even functions are symmetrical about the y-axis.

• If f( -x)= - f(x) , then f(x) is odd

Odd functions have half-turn symmetry about the origin.

Test for even

`f(-x)=-4sin(-x)`

`color(orange)"Reminder " color(red)(|bar(ul(color(white)(a/a)color(black)(sin(-x)=-sinx)color(white)(a/a)|)))`

`rArrf(-x)=-4sin(-x)=4sinx`

Since f(x) ≠ f( -x) , then f(x) is not even.

Test for odd

`-f(x)=-(-4sinx)=4sinx=f(-x)`

Since f( -x) = - f(x) , then f(x) is an odd function.
graph{-4sinx [-10, 10, -5, 5]}