Test y 4x2x2 1 for symmetrySolutiony 4x2x21 for symmetry a

Test y = 4x^2/x^2 + 1 for symmetry.

Solution

y =4x²/(x²+1)

for symmetry about y axis:

put -x in place of x

y=4(-x)²/((-x)²+1)

y=4x²/(x²+1) we get same equation. so curve is symmetric about y axis

for symmetry about x axis

put -y in place of y:

-y =4x²/(x²+1)

equation is not same as original one

so not symmetric about x axis

for symmetry about origin

put -y in place of y:, -x in place of x

-y =4(-x)²/((-x)²+1)

-y =4(x)²/(x²+1)

equation is not same as original one

so not symmetric about origin