If f(x) is an even function and passes through the point (5, 3), what other point must lie on the graph of the function?
f(x) is even if f(-x) = f(x)
so (-5,3) is also on the graph.
If f(x) is an even function and passes through the point (5, 3), it means that for every point (x, y) on the graph, the point (-x, y) must also be on the graph.
Since the point (5, 3) is on the graph, we know that (-5, 3) must also be on the graph.
Therefore, the other point that must lie on the graph of the function is (-5, 3).
An even function is symmetric about the y-axis, which means that its graph is the same on both sides of the y-axis. In other words, for every point (x, y) on the graph of f(x), the point (-x, y) will also be on the graph.
Since the function f(x) passes through the point (5, 3), we can conclude that (-5, 3) must also be on the graph of f(x). This is because (-5, 3) is the reflection of (5, 3) across the y-axis.
So, if f(x) is an even function and passes through the point (5, 3), the other point that must lie on the graph is (-5, 3).