Explanation:
The point (10, 100) lies on the graph of the parent function y = f(x).
To find the point that must lie on the graph of y = 3f(x), we need to multiply the y-coordinate of the given point by 3.
Therefore, the point that must lie on the graph of y = 3f(x) is (10, 300).
Reasons:
1. When multiplying a function by a constant, such as 3 in this case, the y-coordinate of every point on the graph gets multiplied by that constant. So, the y-coordinate of the point (10, 100) on the parent function gets multiplied by 3 to become 300, resulting in the point (10, 300) on the graph of y = 3f(x).
2. The point (10, 100) lies on the graph of the parent function y = f(x), meaning that when x = 10, y = 100. Since y = 3f(x), when x = 10, y = 3f(10). Therefore, y = 3(100) = 300, so the point (10, 300) must lie on the graph of y = 3f(x).