Question

1. The graph of the equation y = x2 – 3 is symmetric with respect to which of the following? The answer is the y-axis . why?

2.The graph of an odd function is symmetric with respect to which of the following? the origin is the answer, why ?

Answer 1

1. symmetric about the y-axis because f(-x) = f(x).
That is, if you pick a point on the graph, flip it about the y-axis, you land on another point on the graph.

2. odd function means f(-x) = -f(x)
Same thinking as above, but (x,y) is matched by (-x,-y). Join the points, and the midpoint of the line is (0,0).