Question

The point (-3,5) lies on the graph of y = f(x). Through which point must the graph of y=+* (3) pass?

O (5,3)
O (5-3)
O (3.-5)
O (-5, -3)

Answer 1

The graph of y=f(-x) must pass through the point (3,5), reflecting the original point across the y-axis by changing the sign of the x-coordinate while keeping the y-coordinate the same.

Step-by-step explanation:

The student asked "Through which point must the graph of y=f(-x) pass, given the point (-3,5) lies on the graph of y = f(x)?" When we substitute x with -x in the function f(x), we must find the point that corresponds to the input of the opposite sign of -3, which is 3. Therefore, we replace x in the point (-3,5) with -x to get the point (3,5), then the graph of y=f(-x) must pass through the point (3,5). It's important to remember that changing x to -x reflects the graph across the y-axis, so the x-coordinate changes sign but the y-coordinate remains the same.