Determine whether the graph of each equation is symmetric with respect to the origin, the x-axis, the y-axis, the line y
x, the line y
x, or none of these x = 5y^2

Question

Determine whether the graph of each equation is symmetric with
respect to the origin, the x-axis, the y-axis, the line y
x, the line
y
x, or none of these.

Answer 1

x=5y^2 is symmetrical about the x-axis, because for every positive value of x except x=0, there are 2 values of y. The x axis acts like mirror and the graph resembles a U lying on its side with its arms pointing to the right (in the positive x direction) and passing through the origin (0,0).