odd and even functions

given this function is there a way in matlab with which i can know is its odd, even or neither?

Answer 1

[Voss]

One thing you can do is to plot the function and visually inspect it:

f = @(x)0.5*(sin(x)+abs(sin(x)));
fplot(f,[-pi pi])

It doesn't look even or odd.

You could also evaluate the function at some values of x and -x and compare the results:

x = -pi:0.1:pi;
is_even = isequal(f(x),f(-x))

is_even = logical
   0

is_odd = isequal(f(x),-f(-x))

is_odd = logical
   0

(A sanity check with functions known to be odd or even)

f = @(x)sin(x);
is_even = isequal(f(x),f(-x))

is_even = logical
   0

is_odd = isequal(f(x),-f(-x))

is_odd = logical
   1

f = @(x)cos(x);
is_even = isequal(f(x),f(-x))

is_even = logical
   1

is_odd = isequal(f(x),-f(-x))

is_odd = logical
   0

[SSBGH]

thanks

[SSBGH]

when i tried to plot it without [-pi pi] i got this

doesn't it look like an even function?

[Voss]

No. An even function is symmetric about the y-axis.

f = @(x)0.5*(sin(x)+abs(sin(x)));
fplot(f,[-15 7.5]);
set(gca(),'YAxisLocation','origin','YLim',[-0.2 2.2])

[SSBGH]

thanks you are great

[Voss]

You're welcome!

Answer 2

[David Hill]

x=-pi:.001:pi;
f=@(x).5*(sin(x)+abs(sin(x)));
if isequal(f(x),f(-x))
    even_odd=2;%even
elseif isequal(-f(x),f(-x))
    even_odd=1;%odd
else
    even_odd=0;%neither
end

[SSBGH]

thanks alot