Determine algebraically whether the graph is symmetric with

Determine algebraically whether the graph is symmetric with respect to the X-AXIS, the y- axis, and the origin. 40) 3x = 3y2 + 4

Solution

To check symmetry with respect to x axis we need to check if changing y to -y changes the equation or not.

So let\'s substitute -y in place of y

3x=3(-y)^2+4=3y^2+4

So the equation remains unchanged hence it is symmetric about x axis

Now to check symmetry about y axis we set x to -x and see if the equation remains unchanged

-3x=3y^2+4

So we see that the equation changes hence it is not symmetric about y axis

To check symmetry about origin we changes x to -x and y to -y and see if the equation remains unchanged

-3x=3(-y)^2+4

-3x=3y^2+4

So we see that equation changes and hence it is not symmetric about origin