Page 58 - Math SL HB Sem 1

FUNCTIONS, IiQUA'tIONS, INE, QU1\LI'I'tES

Example 2
On the same set of axes, sketch the graph of
a)f(r)=x'1,y=f(2x)
b).f(,)=G,y=qf7)

(use GDC)

3.I{cflectinn s

a) lteflcction about thc x-axis
v
(x, y)

0 x' x
(x v -v' v

when reflecting about the x-axis we observe that the coordinates (x, y) are mapped to the
coordinates (x, -y). Meaning that the x-valucs remain the same but the y-values change sign

b) Ileflcction about the y-a ts
v
C*''y')r---- { (x, y)
! x' = -x
v !'
x

when reflecting about the y-axis we observe that th.: coordinate (x,y) is mapped to the
coordinate (-x, y)- Meaning that the y-values remain the same but the x-valucs change sign,

The effects olthese two transformations olthe graph ofy - f(x)
l. y - - f(x), represents a reflection off(x) about the x-axis.
2. y - (-x), represents a reflection off(x) about the y a.ris.

j-t2