Page 54 - Math SL HB Sem 1

FUNC'IIONS, IiQTIATIONS, INIiQUALITIES

TI{ANST'OITMATIONS OF GRA PI IS

l.Translation

a) Vertical translat ion

The graph of y= f(x)+b is a translation ol the graph y- f(x)by D units parallel to the y

axts
l. If b > 0, then the function value o.aluared at X,, is + b , and it exceetls
.t QY ,,) t6 ,) by
b
ii. Il b <0, the

v .y= I + (x)

Yr* llx)

i
.ii + {xo)
I ,(xo
x
0 "o

b) Horizontal translation

The graph of y - J'(.x a) is a translation of the graph of y = f(x) by n units parallel to the x-
AXIS.

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

)' \,
v = (x) y: {lx * a}

^"--- x
0 € x

l8