The graph of y= f(x) is shown. Draw the graph of y=2f(x-1)

Question

The coordinates are (0,0) (-2,-4) (4,-2) for the original graph. It has to be transform into new coordinates. I don’t understand

Answer 1

x f(x)

0 0

-2 -4

4 -2

You need to draw y = 2 f (x-1)

So you need to choose x so that x-1 = 0, -2, 4 then you can use the above values

New function

x-1 = 0, x = 1, y = 2 f (x-1) = 2 f(0) = 2 x 0 = 0

x-1 = -2 x = -1 y = 2 f (x-1) = 2 f(-2) = 2 x -4 = -8

x-1 = 4 x = 5 y = 2 f (x-1) = 2 f (4) = 2 x -2 = -4

So 3 points on the new graph are (1, 0) (-1, -8) and (5, -4)

Basically going from y = f(x) to y = f(x-a) where a is a constant positive number you translate (move) y = f(x) a units to the right.

y = f(x) to y = 2 f(x), you dilate f(x) with center (0,0) factor 2, so (a,b) > (2a, 2b)

So basically here you are doing both things.

So if (a,b) is on y = f(x) then after the translation (a,b) > (a+1, b) then after the dilation (a+1,b) > (2a+2, 2b)