Recall our discussion of symmetry in class. The graph of an equation is symmetric with respect to the $x$-axis if $(x,-y)$ is on the graph whenever $(x,y)$ is. It is symmetric with respect to the $y$ axis if $(-x,y)$ is on the graph whenever $(x,y)$ is. And it's symmetric with the respect to the origin if $(-x,-y)$ is on the graph whenever $(x,y)$ is.
For example, the graph of $y=x^2$ is symmetric with respect to the $y$ axis since if we replace $x$ with $-x$ we obtain the same $y$. Similarly, the graph of $x=y^2$ is symmetric with respect to the $x$-axis. The graph of $y = x^3$ is symmetric with respect to the origin because we get $-y$ when we replace $x$ with $-x$. On the other hand, the equation $y = x+1$ is not symmetric in any of these three senses.
Below, enter x if the graph of the given equation is symmetric with respect to the $x$-axis, $y$ if it is symmetric with respect to the $y$ axis, o (lower case O) if it is symmetric with respect to the origin, and n (for None) if it has none of these three symmetries.

$y=x+1$
$y=x^3$
$y=x^2$
$x=y^2$