If the graph of an equation is symmetric with respect to the origin and -7 is a y-intercept of this graph, name another y-intercept.

Question

The known y-intercepts of the graph described above are -7 and

Answer 1

Hi Steven,

Timothy's answer that the other y-intercept is (0,7) is correct, however, an equation being "symmetric with respect to the origin" does not necessarily mean that the equation must be a circle. Being "symmetric with respect to the origin" means that every point on the graph has another corresponding point on the graph on the opposite side of the origin, 180° away, at the same distance. This is also known as "odd" symmetry:

f(-x) = -f(x)

(As opposed to "even" symmetry, where every point on the graph has a corresponding point on the other side of the y-axis):

f(-x) = f(x)

For example, f(x) = sin(x) has odd symmetry, while f(x) = cos(x) has even symmetry.