Question

If (4,2) is a point on the graph of y=f(x), which of the following points must be on the graph of y=f(2x).

a) (4,1)
b) (8,2)
c) (2,2)
d) (4,4)

Answer 1

we know that 4 = f(2) = f(2*1)
so, (a)

we know nothing about f(4) or f(8)

Answer 2

If (4,2) is on the graph, then f(4) = 2. Let's replace the 4 with 2x and see if we can get that 2x to equal 4, since we know the f(4). Well, when x = 2, then 2x = 4. Therefore, f(2x) is the same as f(4), which we know = 2. So, when x = 2, then f(2x) = 2, and we have the point (2,2).