Final answer:
Option A. The corresponding point on g(x) = f(x) - 3 for the point (4, 2) on f(x) is (4, -1). So, the new y-coordinate will be 2 - 3, which is -1. Thus, the point on g(x) that corresponds to the point (4, 2) on f(x) is (4, -1).
Step-by-step explanation:
If f(x) has a point at (4, 2), then to find the corresponding point on g(x) = f(x) - 3, we simply subtract 3 from the y-coordinate of the point on f(x). The x-coordinate will remain unchanged because the transformation only affects the y-values. So, the new y-coordinate will be 2 - 3, which is -1. Thus, the point on g(x) that corresponds to the point (4, 2) on f(x) is (4, -1).
If the function f(x) has a point at (4, 2), and you want to find the corresponding point on the function g(x) = f(x) - 3, you subtract 3 from the y-coordinate of the point on f(x). This is because g(x) takes the output value from f(x) and decreases it by 3. Therefore, the y-coordinate for the point on g(x) will be 2 - 3, which equals -1, and the x-coordinate will remain the same, which is 4. The point on g(x) will then be (4, -1), which corresponds to option A.