~symmetry~ even?odd? odd even? even odd? @@!

So, now we're gonna look at how is symmetry represented in the equation of a polynomial function. There are so many things around us that are in symmetry. Here's few of them:

 The symmetry for a polynomial function can either be a line symmetry or a point symmetry. But the question is how do we determine which one is for which?

Even Function = LINE SYMMETRY about x=0 Odd Function = POINT SYMMETRY about the origin

Remember that not every even degree functions are even functions!! An even degree polynomial function may be an odd function!

Now, let us look at the table below :

How is symmetry represented in the equation of a polynomial function?
EVEN             y  =  x⁴- 8x² An even function always has line symmetric about the y-axis / at x = 0 HOW TO KNOW WHETHER y = x⁴-8x²  IS AN EVEN FUNCTION?? Let f(x) =  x⁴-8x² F(-x) =   (-x)⁴-8(-x)²          =  x⁴-8x² SINCE f(x) = f(-x), f(x) IS AN EVEN FUNCTION!	ODD 1)      y = x³-4x An odd function always has a point symmetry about the origin (0,0) HOW TO KNOW WHETHER y = x³-4x  IS AN ODD FUNCTION?? Let f(x) = x³-4x f(-x) = ( -x)³-4(-x)          = -x³+ 4x          = -(x³-4x) SINCE -f(x) = f(-x), f(x) IS AN ODD FUNCTION!