Page 56 - Math SL HB Sem 1

FUNCTTONS, EQUA'rrONS, TNEQUALTTtlts

Example 3
Using translations on the graph of (i = Ji,sketch the graph of the follorving
,f
a)y=f(x-4) (useGDC)
b) y = f(x')-2
c) y = f(x-2)+3

2. Stretching or Dilations
a) Stretching fronr the x-itxis.

-
The equation y pf (x) can be written as I - .f O). Jhe tcrm Z represents a
pp
transformation on the y .. axis as opposed to a transformation on the graph of /(-r) _ The

effect ol 'p' in the ternr Z i. thut ofdilution lrom the x-axis.
p

For the curve with equation y pf(x), the effects on the graph of f(x).
=
l. If lpltl,."pr"r"nts'stretching' f(r) bya factorpfromthex-axis.

2. If 0<lpl < l, represents 'shrinking' f(x)by afactor I from rhe x-axis.
p

The relationship between the originat coordinates (x, y) and the new coordinates (xr, yr)
can be seen in the diagram belorv.

(*''y') here x x
1 v pv
p
?
,v)
I x

3- l0