h2 graphing techniques

yok23 SG

1. a curve y=f(x) undergoes , in succession, the following transformations:

A: a translation of magnitude 2 units in the direction of the x axis

B: a scaling parallel to the x axis by a factor of 1/2

C: a reflection in the y axis

D: a translation of magnitude 1 unit in the direction of the y axis.

The resulting curve has the eqn y=1+ e^(2(x+1)). determine the eqn of the curve before the four transformations were affected.

(ans is y=e^(-x), but i cant get it)

2. I'm also very confused where sometimes a graph makes a sharp turn whereas sometimes it makes a round turn, when a graph undergoes transformations. can anybody explain to me in which circumstances must use which one, cos the qn are all very similar.

wee_ws SG

Hi,

For transformations involving the equation of a curve, it is worthwhile to recall the following points:

A. Translation of a units right : replace x with x - a.

B. Scaling of factor 1/a parallel to the x-axis: replace x with ax.

C. Reflection in the y-axis: replace x with -x.

D. Translation of a units up: replace y with y - a.

To obtain the equation of the curve before transformations, we'll have to reverse the actions in this sequence: D (replace y with y + a, since the reverse is to translate a units down), C (figure out on your own), B (figure out on your own), A (figure out on your own).

For your second query, it is not clear what transformations you are referring to.

Thanks.

Cheers,
Wen Shih