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

2 Answers
Sep 4, 2016

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.

Sep 4, 2016

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]}