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? Explain your reasoning.
To understand which other point must lie on the graph of an even function given that it passes through a specific point, we need to consider the symmetry of even functions.
An even function is symmetric with respect to the y-axis, which means that if (a, b) is on the graph of the function, then (-a, b) must also be on the graph. In other words, if a point (x, y) lies on the graph of an even function, then the point (-x, y) must also be on the graph.
Given that f(x) is an even function and it passes through the point (5, 3), we can infer that (-5, 3) must also lie on the graph. By applying the symmetry property of even functions, we reflect the given point across the y-axis to obtain an additional point on the graph.
Therefore, the other point that must lie on the graph of the function f(x) is (-5, 3).