If the point (2, 3) is on the graph of y=f(x), find the coordinates of a point on the transformed function y=2f(3x-1)+5.

Question

If the point (2, 3) is on the graph of y=f(x), find the coordinates of a point on the transformed function y=2f(3x-1)+5..

Answer 1

(2, 3) can be written as f(2) = 3

In y=2f(3x-1)+5, if x=1 then f(3x-1) = f(2).

3x-1 = 2

3x = 3

x=1

So let's plug in x=1 to the transformed function:

y=2f(3*1-1)+5

y=2f(2)+5

since f(2) = 3, then

y=2(3)+5

y = 11

Therefore the point we are looking for is (1,11).