what would be another point of the graph?

Question

1) if an even function passes through the point (1,2), what would be another point on the graph?

2) if an odd function passes through the point (-5,7), what would be another point on the graph?

Answer 1

If y = f(x) is even, then the graph is symmetric to the y-axis. So, since (1,2) lies on the graph, so does (-1,2).

If y = f(x) is odd, then the graph is symmetric to the origin. So, since (-5,7) is on the graph, so is (5,-7).