The derivation of one equation from another

[yojoe]

In each case below explain how the graph of the first equation can be obtained from the graph of the second one by a sequence of shifts and/or stretching. Be careful to write down the sequence in the right order.

a) y=3(x-2)^4 from y=x^4

b) y=2x^2 -2x from y=x^2

c) y=3sin(x/2) from y=sinx


For the first one (a) I'm getting 1) a shift to the right 2 units, 2) and then a stretch of three units

For the second one (b) I'm getting 1) a shift down of 2 units, 2) and then a stretch of 2 units

For the third one, (c) I'm guessing 1) a shift of 1/2 units to the left, 2) and a change in max to 3 and min to -3

Am I going about this the right way? Do these sound correct?
This is my first time here, thanks in advance.

 

[tkhunny]

b) y=2x^2 -2x from y=x^2
For the second one (b) I'm getting 1) a shift down of 2 units, 2) and then a stretch of 2 units

2x^2 - 2x = 2(x^2 - x) = 2(x^2 - x + ¼) - 2(¼) = 2(x-½)^2 - ½

Does this cause you to change your opinion?

c) y=3sin(x/2) from y=sinx
For the third one, (c) I'm guessing 1) a shift of 1/2 units to the left, 2) and a change in max to 3 and min to -3

No shift. That 2 does something else. You tell me.