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]}