Analysis and Approaches HL Practice Paper Book | Page 16

Your Practice Paper – Analysis and Approaches HL for IBDP Mathematics

� Summary of transformations :

x f ( x) � f ( x)

� k :

Translate upward by k units f ( x) � f ( x)

� k : Translate downward by k units f ( x) � f ( x � h)

:

Translate to the left by h units f ( x) � f ( x � h)

: Translate to the right by h units f ( x) � kf ( x)

: Vertical stretch of scale factor k f ( x) � f ( kx)

: Horizontal compression of scale factor k

f ( x) �� f ( x)

:

Reflection about the x -axis f ( x) � f ( � x)

: Reflection about the y -axis

ax � b

� Properties of rational function y � cx � d ^:

1

1 . y � : Reciprocal function x a

2 . y � : Horizontal asymptote c d

3 . x �� : Vertical asymptote c

� Odd and even functions : f( x ) is odd if f ( �x) � � f ( x) f( x ) is even if f ( �x) � f ( x)

4

SE Production Limited