Page 54 - Math SL HB Sem 1

FUNC'IIONS ItQtJ,tl tONS, rNITQUAr,r'I IES
,

TRANSFORMATIONS OF C;ItAPIIS

l.Translation

a) Vertical transl:rt ion

The graph of y .f(x) +bis a translation ol rhe graph y - f(*)by b units parallel to rhe y
ax rs
If 6 > 0, then the function value er.aluated at X,, is + b , and it exceetls
[(X ,,) f(X,,) by
b
ll. IID<0,the

y=h+l\x\
v

v -- \x)

I
I lt
ii r (xo)
I (xo)
x
0

b) Ilorizo n ta I translatiorr

The graph ol y- (x o) is a translario. of the graph of y= [(x) by a units parallel to the x-
f -
ax rs.

-
The origin of the X Y plane lies at the point (a, 0) of the x-y plane. The graph
y = f(x-a) = /(x) drawn on the X,Y plane is the same as the graph of y - f(x) drawn on the
x - y plane- Thus, il r.ve move the graph of y = (x) a distance n to the right, we ger the graph
of y=f(x-a) "f

)' )'
-
y {(x) y= l(x al
=

-"-- - x
0 a .Y