Page 57 - Math SL HB Sem 1

I,'TJNCT'I()NS IIQtJ:\'l'l0Ns , tNEQI rr\LI',l'tlis
,

b) Stretching from the y-axis.

/\
Thc equation : f l{ | ,.pr"r"n,, a transrormarion appried to t}re x-varues. The tcnn I
v
'"
\q ) I aPP'rE(i tu trrq x-valucs l ne
: tl
represents a transformation on the x- varues as opposed to a transformation on the graph of f (x).
{
The effect of 'q' in term
is that of dilation from the y_axis.
q
/ )
For the curve with equation y = t ' , rhe effccr on the graph of t1x)
I ; ]
l. If > ,
lql I, represenls stretching, (x) by a factor q liom the y_axis,
2. IfO < < ,
lq | l, represents shrinking, f(x) by a factor -l from the y_axis.
q
-[he

relationship between the originar coordinates (x, y) and the new coordinates (xr,yr) can be
seen in the diagram below.
v

Where: xr ,= I
q_ > q
y =y
(x. y) (*' y')
,
x

Iixam lcl
Given Lhe graph ol y
= -t(x). Skerch rhe graph o[ v
a) y =2f (x) (0,3)
b) 3y = f(x) v=f (x)
c) y = f(2x)
,I
at y = f(I)
-2 4

(6,-t )

.i-l I