91Ó°ÊÓ

To find the x-intercept, set y to 0 and solve the equation for x. In our case, \(x = 0^{2} - 1 = -1\).\nTo find the y-intercept, set x to 0 and solve the equation for y. In our equation, we have no real value of y when x=0, because there are zero real number solutions to the equation \(0 = y^{2} - 1\). Therefore, the graph does not intersect the y-axis.

There are three types of symmetry to test for: symmetry about the y-axis, symmetry about the x-axis, and symmetry about the origin.\n1. To test for symmetry about the y-axis, replace x with -x and see if the equation is still true. Our equation \(x = y^{2} - 1\) becomes \(-x = y^{2} - 1\), which is not the same equation, so it's not symmetrical around the y-axis.\n2. To test for symmetry about the x-axis, replace y with -y. But \(x = (-y)^{2} - 1\) simplifies to \(x = y^{2} - 1\), which is the original equation, so it's symmetrical about the x-axis.\n3. To test for symmetry about the origin, replace both x and y with -x and -y respectively. But \(-x = (-y)^{2} - 1\) simplifies to \(-x = y^{2} - 1\), which is not the same as our original equation, so it's not symmetrical around the origin.

The graph of the equation can be plotted using the above information (intercepts and symmetry).\nThe graph will be a parabola opening to the right, as \(x = y^{2} - 1\) is of the form \(x = y^{2}\), and it will be shifted 1 unit to the right due to the -1 in the equation. It will not intersect the y-axis, but it will intersect the x-axis at x=-1. The graph will be symmetrical with respect to the x-axis as established above.