Page 56 - Math SL HB Sem 1

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Example 3
Using translations on the graph of f(t) - Jt ,sketch the graph ofthe lollorving
a) y=f(x-4) (useGDC)
b) y=f(x)-2

c) y = f(x-2)+3

2. Stretc h ing or Dilations
a) Stretching from the x-axis.

The equation y = 1tf (x) can be written us ! = f(r). J'hc term Z represents a
pp

transformation on the y axis as opposed to a transformation on the graph of /(_r) The
Z
effect of 'p' in the ternr is thal ofdilation from the x-axis.
p

-
For the curve with equation y pf(x), the effects on the graph of f(x).
l. If lpl,I,."pr"t"nts'stretching' fG) bya factorp fromthex-axis.

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

The relationship between the original coordinates (x, y) and the new coordinates (xr, yi)
can be seen in the diagram below.

(* y') Where x :pv
''
v
?
(*, v)
x

3-t0