 1 - Algebra and functions

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1 - Algebra and functions
1 DOMAIN
2 RANGE
3 MAPPING
3.1 ONE-ONE
3.2 MANY-ONE
3.3 ONE-MANY
3.4 MANY-MANY
4 FUNCTION
4.1 CONDITIONS
4.1.1 DEFINED
4.1.1.1 ALL ELEMENTS
4.1.2 EITHER
4.1.2.1 ONE-ONE
4.1.2.2 MANY-ONE
4.2 COMPOSITE
4.2.1 fg(x)
4.2.1.1 g(x)
4.2.1.1.1 f(g[x])
4.3 INVERSE
4.3.1 ONE-ONE
4.3.2 DOMAIN = RANGE

Annotations:

• DOMAIN OF f^-1 = RANGE OF f
4.3.3 RANGE = DOMAIN

Annotations:

• RANGE OF f^-1 = DOMAIN OF f
4.3.4 CHANGE SUBJECT

Annotations:

• MAKE x SUBJECT; THEN REWRITE "SWAPPING" x 's AND y 's (OR f(x) 's)
5 TRANSFORMATIONS
5.1 TRANSLATIONS

Annotations:

• y = f(x) + a translation by a units in y-direction
• y = f(x + a) translation by -a units in x-direction
5.2 STRECHES

Annotations:

• y = a f(x) stretch by scale factor a in y-direction
• y = f(a x) stretch by scale factor 1/a in x-direction
5.3 REFLECTIONS

Annotations:

• y = -f(x) reflection in x-axis
• y = f(-x) reflection in y-axis
6 MODULUS
6.1 POSITIVE
7 EXPONENTIAL
7.1 e
7.2 ln