Question

Given that (8,4) is on the graph of f(x), find the corresponding point for the function f(4x).

Answer 1

The given point is (8,4) which means we know f(8) = 4. 

We don't know any outputs for f(4x) other than the output of 4 which was stated with f(8) = 4. So f(4x) = 4 for some input x. In order for 4x to be equal to 8, that x value must be 2. 

f(4x) = f(8)
f(4*2) = f(8)

So the point (2,4) is on the graph of f(4x)
Plugging in x = 2 leads to f(4x) = f(4*2) = f(8) = 4

Answer 2

$\bf \stackrel{f(x)}{(8~~,~~4)}\qquad \qquad \qquad \stackrel{f(4x)}{(4(8)~~,~~4)}\implies (32,4)$