Check the Symmetry

Symmetry is nothing but Quality of being made of the precisely similar parts

Nature loves symmetry

Now we will check the symmetry

1)

if the curve is symmetrical about the x-axis

a)Y will be replaced by (-y), and curve remains the same

for example, y2=x represents the parabola which is symmetrical about the x-axis

proof: replace y with -y in the above equation

(-y)2=x⇒y2=x so the curve remains same

2)

if the curve is symmetrical about the y-axis

a) f(-x)=f(x) means curve should be even function

for example, x2=y represents the parabola which is symmetrical about the y-axis

proof: replace x with -x in the above equation

(-x)2=y⇒x2=y so the curve remains same

(-x)²=y⇒x²=y so the curve remains same 

3)

if the curve is symmetrical about the line y=x

on interchanging of x and y Curve remains the same

For example, Cubic function y=x3 is symmetrical about the line y=x

let us interchange the x and y

⇒x=y3

Solve for y=x1/3 below given graph are two graphs which are symmetrical about the line y=x