Page 58 - Math SL HB Sem 1

FUN(11'IONS, EQU.,lt'l'IONS, I NEQtI;\1.11-l ES

Example 2
On the same set ofaxes, sketch the graph ol
a) "f(x)= x'1, y = f(2x)
b),f(:)-Ji,y-qf7)

(use GDC)

3.I{cflections

a) Ileflcction about the x-axis
v
(x, y)

0 x x
(r', -y') v v

When re{Iecting about the x,axis wc observe that the coordinates (x, y) are mapped to the
coordinates (x, -y). Meaning that the x-values remain the sarne but the y-values change sign.

b) Reflcction about the y-:r rs
v
(-*''y')f---- --{ (x, v)
xl : -*
yl: y

x

When reflecting about the y-axis we observe that the coordinate (x,y) is mapped to the
coordinate (-x. y)- Meaning that the y-values remain the samc but the x-values change sign.

The effects ofthese two transfonnations of the graph of y - f(x)
l . y : - f (x), represents a reflection of f(x) about rhe x-axis.
2. y : f(-x), represents a reflection off(x) aboLrt the y axis.

i- l2