if F(x) is an even function and the point (-5,3) lies on the graph of F(x), identify an additional point on the graph.

Answer 1

Even function means that the function is symmetric according the y-axis. If a point with coordinate (x, y) is on the graph, then the point (-x, y) is on the graph also. That is, the point with the opposite value of coordinate x and y are on the graph.

Our point is ( -5, 3). Then what is the opposite of -5?

The point with this x and same y coordinate will be on the graph.

Questions?

Answer 2

Because F(x) is even F(-x) = F(x). So if point (-5,3) lies on the graph then F(- 5) = 3 and F(5) = 3.

So point (5,3) also lies on the graph F(x).