ⵜⴰⵙⵖⵏⵜ (ⵜⵓⵙⵏⴰⴽⵜ)

ⵜⴰⵙⵖⵏⵜ (ⵙ ⵜⵏⴳⵍⵉⵣⵜ: function), ⴳ ⵜⵓⵙⵏⴰⴽⵜ, ⵜⴳⴰ ⵢⴰⵏ ⵓⵍⵓⴳⵏ ⵉⵣⴷⴰⵢⵏ ⴽⵓ ⴰⴼⵔⴷⵉⵙ ⵙⴳ ⵜⴳⵔⵓⵎⵎⴰ ⵜⴰⵎⵣⵡⴰⵔⵓⵜ, ⵉⵜⵜⵓⵙⵎⵎⴰⵏ ⵜⴰⵖⵓⵍⵜ, ⵙ ⵢⴰⵏ ⵓⴼⵔⴷⵉⵙ ⴰⵎⵢⵉⵡⵏ ⵙⴳ ⵜⴳⵔⵓⵎⵎⴰ ⵜⵉⵙⵙ ⵙⵏⴰⵜ, ⵉⵜⵜⵓⵙⵎⵎⴰⵏ ⵜⴰⵣⴷⴰⵖⵓⵍⵜ. ⵉⴳⴰ ⵓⵔⵎⵎⵓⵙ ⵏ ⵜⵙⵖⵏⵜ ⴰⵔⵙⵍⴰⵏ ⴳ ⵓⵎⴰⵜⴰ ⵏ ⵉⴳⵔⴰⵏ ⵏ ⵜⵓⵙⵏⴰⴽⵜ ⴷ ⵜⵓⵙⵙⵏⵉⵡⵉⵏ ⵢⴰⴹⵏⵉⵏ. ⵜⵓⵇⵇⵏⴰ ⴰⴷ ⴷⴰ ⵜⴻⵜⵜⵓⵙⴽⴰⵏ ⴳ ⵓⵎⴰⵜⴰ ⵣⵓⵏ ⴷ "ⵜⴰⵎⴰⵛⵉⵏⵜ" ⵉⵜⵜⴰⵎⵥⵏ ⵜⵉⵏⴽⵛⵓⵎⵉⵏ (ⴰⴼⵔⴷⵉⵙ ⵙⴳ ⵜⴰⵖⵓⵍⵜ) ⵜⴼⴽ ⵜⵓⴼⴼⵖⴰ ⵜⴰⵎⵢⵉⵡⵏⵜ (ⴰⴼⵔⴷⵉⵙ ⵏ ⵜⵣⴷⴰⵖⵓⵍⵜ). ⵙ ⵓⵎⴷⵢⴰ, ⵜⴰⵙⵖⵏⵜ ⵍⵍⵉ ⵉⵣⴷⴰⵢⵏ ⴽⵓ ⴰⵎⴹⴰⵏ ⴰⵏⵉⵍⴰⵡ  ⵙ ⵓⵎⴽⴽⵓⵥ ⵏⵏⵙ  ⵜⴳⴰ ⵜⴰⵙⵖⵏⵜ.

 ⴰⵙⵏⵎⵍ ⴰⵍⵖⴰⵏ 

ⵉⴱⴷⴷ ⵓⵙⵏⵎⵍ ⴰⵍⵖⴰⵏ ⵏ ⵜⵙⵖⵏⵜ ⵖⴼ ⵓⵔⵎⵎⵓⵙ ⵏ ⵜⵢⵓⴳⵉⵡⵉⵏ ⵉⵏⵎⴰⵍⴰⵏ. ⵜⴰⵙⵖⵏⵜ  ⵙⴳ ⵜⴳⵔⵓⵎⵎⴰ  (ⵜⴰⵖⵓⵍⵜ) ⵖⵔ ⵜⴳⵔⵓⵎⵎⴰ  (ⵜⴰⵣⴷⴰⵖⵓⵍⵜ) ⵜⴳⴰ ⵢⴰⵜ ⵜⴳⵔⵓⵎⵎⴰ ⵏ ⵜⵢⵓⴳⵉⵡⵉⵏ ⵉⵏⵎⴰⵍⴰⵏ  ⵍⵍⵉ ⴳ ⵉⴳⴰ  ⴰⴼⵔⴷⵉⵙ ⵙⴳ  ⴷ  ⵉⴳⴰ ⴰⴼⵔⴷⵉⵙ ⵙⴳ , ⵙ ⵜⴼⴰⴷⴰ ⵏ ⴰⴷ ⵢⵓⵎⴰⵏ ⴽⵓ ⴰⴼⵔⴷⵉⵙ  ⴳ  ⵢⴰⵜ ⵜⴽⴽⵍⵜ ⵀⵍⵍⵉ ⴰⵎⵎ ⵉⵙⴳⵔ ⴰⵎⵣⵡⴰⵔⵓ ⴳ ⵜⵢⵓⴳⴰ. ⴷⴰ ⵜⴻⵜⵜⵢⴰⵔⴰ ⵜⵓⵇⵇⵏⴰ ⴰⴷ ⵙ ⵉⵎⴽⴰ . ⵉⴳ ⵉⵍⵍⴰ  ⴳ ⵜⵙⵖⵏⵜ , ⴷⴰ ⵏⵜⵜⵉⵏⵉ ⵎⴰⵙ ⴷ  ⵜⴳⴰ ⵜⵓⴳⵏⴰ ⵏ  ⵙⴳ , ⵏⴰⵔⴰ .


ⵜⴻⵜⵜⵓⵙⵎⵎⴰ ⵜⴳⵔⵓⵎⵎⴰ ⵏ ⵡⴰⵣⴰⵍⵏ ⴰⴽⴽⵯ  ⵍⵍⵉ ⵏⵥⴹⴰⵕ ⴰⴷ ⵏⴰⴼ ⵜⵓⴳⵏⴰ ⵏ ⵜⵙⵖⵏⵜ  ⵏⵖ ⴰⵣⵉⵍⴰⵍ ⵏⵏⵙ. ⵉⵇⵇⴰⵏ ⴷ ⴰⴷ ⵓⵔ ⵏⵙⵎⵔⴽⴰⵙ ⴳⵔ ⵜⵓⴳⵏⴰ (ⴰⵣⵉⵍⴰⵍ) ⴷ ⵜⵣⴷⴰⵖⵓⵍⵜ. ⵜⴰⵣⴷⴰⵖⵓⵍⵜ ⵜⴳⴰ ⵜⴰⴳⵔⵓⵎⵎⴰ  ⵍⵍⵉ ⴳ ⵥⴹⴰⵕⵏ ⴰⴷ ⵉⵍⵉⵏ ⵡⴰⵣⴰⵍⵏ ⵏ ⵜⵓⴼⴼⵖⴰ, ⵎⴰⵛⴰ ⵜⵓⴳⵏⴰ (ⴰⵣⵉⵍⴰⵍ) ⵜⴳⴰ ⵜⴰⴳⵔⵓⵎⵎⴰ ⵏ ⵡⴰⵣⴰⵍⵏ ⵏ ⵜⵓⴼⴼⵖⴰ ⵍⵍⵉ ⵏⵉⵜ ⵉⴳⴰⵏ ⵜⴰⵢⴰⴼⵓⵜ. ⵙ ⵓⵎⴷⵢⴰ, ⴳ ⵜⵙⵖⵏⵜ , ⵉⴳ ⵜⴳⴰ ⵜⴰⵖⵓⵍⵜ ⴷ ⵜⵣⴷⴰⵖⵓⵍⵜ ⵜⴳⵔⵓⵎⵎⴰ ⵏ ⵉⵎⴹⴰⵏⵏ ⵉⵏⵉⵍⴰⵡⵏ , ⵀⴰⵜ ⴰⵣⵉⵍⴰⵍ (ⵜⵓⴳⵏⴰ) ⵉⴳⴰ ⵜⴰⴳⵔⵓⵎⵎⴰ ⵏ ⵉⵎⴹⴰⵏⵏ ⵉⵏⵉⵍⴰⵡⵏ ⵓⵎⵏⵉⴳⵏ , ⵍⵍⵉ ⵉⴳⴰⵏ ⵖⴰⵙ ⴰⴳⵣⵣⵓⵎ ⵙⴳ ⵜⵣⴷⴰⵖⵓⵍⵜ.

 ⵜⵉⵔⵔⴰ 
ⵍⵍⴰⵏⵜ ⵎⵏⵏⴰⵡⵜ ⵜⵖⴰⵔⴰⵙⵉⵏ ⵏ ⵜⵉⵔⵔⴰ ⵏ ⵜⵙⵖⵏⵉⵏ. ⵜⴰⵖⴰⵔⴰⵙⵜ ⴰⴽⴽⵯ ⵉⵜⵜⵓⵙⵙⴰⵏⵏ ⴳⴰⵏⵜ ⵜⵜ ⵜⵉⵔⵔⴰ ⵜⵉⵙⵖⵏⴰⵏⵉⵏ, ⵣⵓⵏ ⴷ f(x), ⵍⵍⵉ ⵉⵙⵙⵎⵔⵙ ⵓⵎⵙⵏⴰⴽⵜ ⵍⵢⵓⵏⴰⵔⴷ ⵓⵍⵔ ⴳ ⵓⵙⴳⴳⵯⴰⵙ ⵏ 1734. ⵖⵉⴷ, f ⵉⴳⴰ ⵉⵙⵎ ⵏ ⵜⵙⵖⵏⵜ, ⴷ x ⵉⴳⴰ ⴰⵎⵙⴽⵉⵍ ⴰⵙⵉⵎⴰⵏ ⵉⵜⵜⴳⵏⵙⴻⵙⵏ ⵢⴰⵜ ⵜⵏⴽⵛⵓⵎⵜ.

ⴷⴰ ⵉⵙⵓⵜⵜⵓ ⵓⵙⵏⴳⵍ ⵏ ⵓⵍⴳⴳⵉ ⵜⴰⵖⵓⵍⵜ ⴷ ⵜⵣⴷⴰⵖⵓⵍⵜ ⵏⵏⵉⵛⴰⵏ. ⴰⴷ ⵏⴰⵔⴰ f: X → Y, ⴰⵏⴰⵎⴽ ⵏⵏⵙ ⵎⴰⵙ ⴷ f ⵜⴳⴰ ⵜⴰⵙⵖⵏⵜ ⵉⵣⴷⴰⵢⵏ ⵉⴼⵔⴷⵉⵙⵏ ⵙⴳ ⵜⴳⵔⵓⵎⵎⴰ X ⵖⵔ ⵜⴳⵔⵓⵎⵎⴰ Y. ⵉⵜⵜⵓⵙⴽⴰⵏ ⵓⵍⵓⴳⵏ ⵢⵓⵜⵜⴰⵏ ⵉⵣⴷⴰⵢⵏ ⴰⵏⴽⵛⵓⵎ x ⴰⴽⴷ ⵜⵓⴼⴼⵖⴰ y ⵙ ⵓⵍⴳⴳⵉ ⵢⴰⴹⵏⵉⵏ: x ↦ y. ⵙ ⵓⵎⴷⵢⴰ, ⵜⵖⵉⵢ ⴰⴷ ⵜⴻⵜⵜⵢⴰⵔⴰ ⵜⵙⵖⵏⵜ ⵏ ⵓⵙⴽⴽⵓⵥ ⵙⴳ ⵉⵎⴹⴰⵏⵏ ⵉⵏⵉⵍⴰⵡⵏ ⵖⵔ ⵉⵎⴹⴰⵏⵏ ⵉⵏⵉⵍⴰⵡⵏ ⵙ: f: ℝ → ℝ, ⵍⵍⵉ ⴳ x ↦ x².

 ⵜⴰⴳⵏⵙⴻⵙⵜ ⵏ ⵜⵙⵖⵏⵉⵏ 
ⵥⴹⴰⵕⵏⵜ ⴰⴷ ⵜⵜⵓⴳⵏⵙⴻⵙⵏⵜ ⵜⵙⵖⵏⵉⵏ ⵙ ⵎⵏⵏⴰⵡⵜ ⵜⵖⴰⵔⴰⵙⵉⵏ:

 ⵙ ⵜⵏⴼⴰⵍⵉⵜ ⵜⴰⵎⵚⵍⴰⴹⵜ 
ⵜⴰⵖⴰⵔⴰⵙⵜ ⴰⴽⴽⵯ ⵉⴷⵓⵙⵏ ⵉ ⵜⴳⵏⵙⴻⵙⵜ ⵏ ⵜⵙⵖⵏⵜ ⵉⴳⴰ ⵜⵜ ⵓⵙⵏⴼⴰⵍⵉ ⴰⵎⵚⵍⴰⴹ (ⵏⵖ ⵜⴰⵏⴼⴰⵍⵉⵜ), ⵍⵍⵉ ⵉⴳⴰⵏ ⴰⵙⴷⴷⵉ ⵏ ⵜⵎⵀⵍⵉⵏ ⵜⵓⵙⵏⴰⴽⵜⴰⵏⵉⵏ ⵖⴼ ⵓⵎⵙⴽⵉⵍ x. ⵙ ⵓⵎⴷⵢⴰ:
f(x) = 3x² - 4x + 2
ⴷⴰ ⵜⴻⵜⵜⴳⵍⴰⵎ ⵜⵏⴼⴰⵍⵉⵜ ⴰⴷ ⴰⵍⵓⴳⵏ ⵉ ⵓⵙⵉⴹⵏ ⵏ ⵜⵓⴼⴼⵖⴰ ⵉ ⴽⵔⴰⵢⴳⴰⵜⵜ ⵜⴰⵏⴽⵛⵓⵎⵜ x ⵉⵜⵜⵓⴼⴽⴰⵏ. ⵜⵜⵓⵙⵎⵎⴰⵏⵜ ⵜⵙⵖⵏⵉⵏ ⴰⴷ ⵜⵉⵙⵖⵏⵉⵏ ⵜⵉⴳⵜⴼⵓⵍⵉⵏ. ⵣⴹⴰⵕⵏⵜ ⵜⵙⵖⵏⵉⵏ ⵢⴰⴹⵏⵉⵏ ⴰⴷ ⴰⵎⵓⵏⵜ ⵜⵉⵎⵀⵍⵉⵏ ⵣⵓⵏ ⴷ ⵜⵉⴽⵕⴷⵉⵙⴽⵜⴰⵏⵉⵏ (sin(x), cos(x)), ⵜⵉⵙⵏⵏⴼⵙⴰⵔⵉⵏ (eˣ), ⵏⵖ ⵜⵉⵍⵓⴳⴰⵔⵉⵜⵎⵉⵢⵉⵏ (log(x)).

 ⵙ ⵓⵎⵙⴽⴰⵏ 
ⴰⵎⵙⴽⴰⵏ ⵏ ⵜⵙⵖⵏⵜ f ⵉⴳⴰ ⵜⴳⵔⵓⵎⵎⴰ ⵏ ⵜⵢⵓⴳⵉⵡⵉⵏ ⵉⵏⵎⴰⵍⴰⵏ (x, f(x)) ⵍⵍⵉ ⴳ ⵉⵍⵍⴰ x ⴳ ⵜⴰⵖⵓⵍⵜ ⵏ f. ⴷⴰ ⵜⵜⵓⴳⵏⵙⴻⵙⵏⵜ ⵜⵢⵓⴳⵉⵡⵉⵏ ⴰⴷ ⵙ ⵜⵇⵉⴼⴰ ⴳ ⵓⵏⴳⵔⴰⵡ ⵏ ⵉⵎⵙⵉⴷⴰⴳⵏ ⵉⴽⴰⵔⵜⵉⵣⵢⴰⵏⵏ, ⵍⵍⵉ ⴳ ⴷⴰ ⵉⵜⵜⴳⵏⵙⴻⵙ ⵓⴳⵍⵍⵓⵙ ⴰⵎⵏⵉⴷⴰⵏ ⴰⵎⵙⴽⵉⵍ x ⴷ ⵓⴳⵍⵍⵓⵙ ⴰⴱⴷⴷⴰⵢ ⴷⴰ ⵉⵜⵜⴳⵏⵙⴻⵙ ⴰⵎⵙⴽⵉⵍ y = f(x). ⴷⴰ ⵢⴰⴽⴽⴰ ⵓⵎⵙⴽⴰⵏ ⴰⵙⴽⵙⵉⵡ ⴰⵎⵥⵕⴰⵡ ⴰⵎⴰⵜⴰⵢ ⵖⴼ ⵓⵎⵓⴳⴳⵉ ⵏ ⵜⵙⵖⵏⵜ, ⵣⵓⵏ ⴷ ⵎⴰⵏⵉ ⴳ ⴷⴰ ⵜⴻⵜⵜⵏⵔⵏⴰⵢ ⵏⵖ ⴷⴰ ⵜⴻⵜⵜⵏⵓⵙⵔⵓ. ⴰⵔⴰⵎ ⵏ ⵓⵣⵔⵉⴳ ⴰⴱⴷⴷⴰⵢ ⵉⴳⴰ ⵢⴰⵜ ⵜⵖⴰⵔⴰⵙⵜ ⵏ ⵓⵙⵙⵉⴷⵜ ⵏ ⵉⵙ ⴷⴰ ⵉⵜⵜⴳⵏⵙⴻⵙ ⵢⴰⵏ ⵓⵎⴽⵏⴰⵡ ⵜⴰⵙⵖⵏⵜ: ⵉⴳ ⵉⵎⵢⴰⴱⴰⵢ ⴽⵔⴰ ⵏ ⵓⵣⵔⵉⴳ ⴰⴱⴷⴷⴰⵢ ⴷ ⵓⵎⵙⴽⴰⵏ ⴳ ⵓⴳⴳⴰⵔ ⵏ ⵢⴰⵜ ⵜⵇⵉⴼⵉⵜ, ⵉⵍⵎⵎⴰ ⴰⵎⴽⵏⴰⵡ ⵓⵔ ⵉⴳⵉ ⴰⵎⵙⴽⴰⵏ ⵏ ⵜⵙⵖⵏⵜ.

 ⵙ ⵜⴼⵍⵡⵉⵜ ⵏ ⵡⴰⵣⴰⵍⵏ 
ⴳ ⵜⵙⵖⵏⵉⵏ ⴷⴰⵔ ⵜⵍⵍⴰ ⵜⴰⵖⵓⵍⵜ ⵢⵓⵜⵜⴰⵏ, ⵏⵥⴹⴰⵕ ⴰⴷ ⵜⵏⵜ ⵏⴳⵙⴻⵙ ⵙ ⵓⵙⵎⵔⵙ ⵏ ⵜⴼⵍⵡⵉⵜ. ⴷⴰ ⵜⵎⵎⴰⵍ ⵜⴼⵍⵡⵉⵜ ⴰⴷ ⵉ ⴽⵓ ⴰⵏⴽⵛⵓⵎ ⴰⵣⴰⵍ ⵏ ⵜⵓⴼⴼⵖⴰ ⵏⵏⵙ. ⵙ ⵓⵎⴷⵢⴰ, ⵉⴳ ⵜⴳⴰ ⵜⴰⵖⵓⵍⵜ {1, 2, 3, 4} ⴷ ⵓⵍⵓⴳⵏ ⵉⴳⴰ , ⵜⴰⴼⵍⵡⵉⵜ ⵔⴰⴷ ⵜⴳ ⵉⵎⴽⴰ:

ⵜⴰⴼⵍⵡⵉⵜ ⵏ ⵡⴰⵣⴰⵍⵏ ⵉ:  
+    1 1 2 4 3 9 4 16

 ⴰⵎⵣⵔⵓⵢ 
ⵉⵏⵏⴼⵍⵉ ⵓⵔⵎⵎⵓⵙ ⵏ ⵜⵙⵖⵏⵜ ⴳ ⵓⵣⵎⵣ. ⵜⵓⴳⴳⵯⴰ ⴷ ⵜⵙⵡⵉⵏⴳⵎⵜ ⵜⴰⵎⵣⵡⴰⵔⵓⵜ ⵏ "ⵜⵓⵇⵇⵏⴰ ⵜⴰⵙⵖⵏⴰⵏⵜ" ⴳ ⵜⵡⵓⵔⵉⵡⵉⵏ ⵏ ⵉⵎⵙⵏⴰⴽⵜⵏ ⵉⴳⵔⵉⴽⵉⵢⵏ ⵉⵇⴱⵓⵔⵏ ⴳ ⵓⵙⴰⵜⴰⵍ ⵏ ⵜⵏⵣⴳⴳⵉⵜ, ⵎⴰⵛⴰ ⵓⵔ ⵜⴰ ⵜⵜ ⵉⵏⵏ ⵉⴽⴽⵉ ⵉⵍⵍⴰ ⵓⵙⵏⵎⵍ ⵏⵏⵙ ⴰⵎⴰⵜⴰⵢ. ⴳ ⵜⴰⵙⵓⵜ ⵜⵉⵙⵙ 14, ⵙⵙⵏⵜⵉⵏ ⵉⵎⵙⵡⵉⵏⴳⵎⵏ ⵣⵓⵏ ⴷ ⵏⵉⴽⵓⵍ ⵓⵔⵙⵎ ⴰⵙⵏⵓⵍⴼⵓ ⵏ ⵉⵎⵙⴽⴰⵏⵏ ⵏ ⵜⵓⵇⵇⵏⵉⵡⵉⵏ ⴳⵔ ⵜⵙⵎⴽⵜⵉⵡⵉⵏ ⵉⵜⵜⵏⴼⴰⵍⵏ, ⴰⵢⵍⵍⵉ ⵉⴳⴰⵏ ⵜⵉⵣⵡⵉⵔⵉ ⵜⴰⵎⵏⵣⵓⵜ ⵏ ⵜⴳⵏⵙⴻⵙⵜ ⵜⴰⵎⵙⴽⴰⵏⵜ ⵏ ⵜⵙⵖⵏⵉⵏ.

ⵜⴻⵜⵜⵓⵙⵎⵔⴰⵙ ⵜⴳⵓⵔⵉ "ⵜⴰⵙⵖⵏⵜ" ⵜⵉⴽⴽⵍⵜ ⵜⴰⵎⵣⵡⴰⵔⵓⵜ ⴷⴰⵔ ⴳⵓⵜⴼⵔⵉⴷ ⴼⵉⵍⵀⵍⵎ ⵍⵉⴱⵏⵜⵣ ⴳ 1673 ⴰⴼⴰⴷ ⴰⴷ ⵉⴳⵍⵎ ⵢⴰⵜ ⵜⵙⵎⴽⵜⴰ ⵉⵣⴷⵉⵏ ⴷ ⵢⴰⵏ ⵓⵎⴽⵏⴰⵡ, ⵣⵓⵏ ⴷ ⵜⵉⵖⵣⵉ ⵏⵏⵙ. ⴳ 1748, ⵉⴼⴽⴰ ⵍⵢⵓⵏⴰⵔⴷ ⵓⵍⵔ ⴰⵙⵏⵎⵍ ⴰⵎⵣⵡⴰⵔⵓ ⵢⴰⵥⵏ ⵉ ⵓⵙⵏⵎⵍ ⴰⵜⵔⴰⵔ: "ⵜⴰⵙⵖⵏⵜ ⵏ ⵜⵙⵎⴽⵜⴰ ⵜⴰⵎⵙⴽⵉⵍⵜ ⵜⴳⴰ ⵜⴰⵏⴼⴰⵍⵉⵜ ⵜⴰⵎⵚⵍⴰⴹⵜ ⵉⵜⵜⵓⵙⵏⴰⵢⵏ ⵙ ⴽⵔⴰ ⵏ ⵜⵖⴰⵔⴰⵙⵜ ⵙⴳ ⵜⵙⵎⴽⵜⴰ ⴰⵏⵏ ⵜⴰⵎⵙⴽⵉⵍⵜ ⴷ ⵉⵎⴹⴰⵏⵏ ⵏⵖ ⵜⵉⵙⵎⴽⵜⵉⵡⵉⵏ ⵉⵣⴳⴰⵏ." ⵉⵎⴰ ⴰⵙⵏⵎⵍ ⴰⵜⵔⴰⵔ, ⵉⴱⴷⴷⵏ ⵖⴼ ⵜⵥⵕⵉ ⵏ ⵜⴳⵔⵓⵎⵎⵉⵡⵉⵏ, ⵉⵙⵔⵙ ⵜ ⵢⵓⵀⴰⵏ ⴱⵉⵜⵔ ⴳⵓⵙⵜⴰⴼ ⵍⵓⵊⵓⵏ ⴷⵉⵔⵉⵛⵍⵉⵜ ⴳ 1837, ⵙⴼⴰⵍⴽⵉⵏ ⵜ ⵉⵎⵙⵏⴰⴽⵜⵏ ⵢⴰⴹⵏⵉⵏ ⴳ ⵜⴳⵉⵔⴰ ⵏ ⵜⴰⵙⵓⵜ ⵜⵉⵙⵙ 19.

 ⵜⵉⴼⵔⵉⵙⵉⵏ ⵜⵉⵙⵉⵍⴰⵏⵉⵏ 
ⵥⴹⴰⵕⵏⵜ ⵜⵙⵖⵏⵉⵏ ⴰⴷ ⵜⵜⵓⵙⵉⵙⵎⵍⵏⵜ ⴳ ⵓⵏⵛⵜ ⵏ ⵜⴼⵔⵉⵙⵉⵏ ⵏⵏⵙⵏⵜ. ⵜⵉⴼⵔⵉⵙⵉⵏ ⴰⴷ ⵜⵉⵣⴰⵍⴰⵏⵉⵏ ⴳⴰⵏⵜ ⵜⴰⵢⵏⴳⵉⵔⵜ, ⵜⴰⴼⵍⴳⵉⵔⵜ, ⴷ ⵜⵙⵏⴳⵉⵔⵜ.

   ⵜⴰⵙⵖⵏⵜ ⵜⴰⵢⵏⴳⵉⵔⵜ: ⴷⴰ ⵜⴻⵜⵜⴳⴳⴰ ⵜⵙⵖⵏⵜ f ⵜⴰⵢⵏⴳⵉⵔⵜ (ⵏⵖ "ⵢⴰⵏ ⵉ ⵢⴰⵏ") ⵉⴳ ⵉⵣⴷⵉ ⴽⵓ ⴰⴼⵔⴷⵉⵙ ⴳ ⵜⵓⴳⵏⴰ (ⴰⵣⵉⵍⴰⵍ) ⴷ ⵢⴰⵏ ⵓⴼⵔⴷⵉⵙ ⴰⵎⵢⵉⵡⵏ ⴳ ⵜⴰⵖⵓⵍⵜ. ⵙ ⵜⵖⴰⵔⴰⵙⵜ ⵢⴰⴹⵏⵉⵏ, ⵉⴳ f(x₁) = f(x₂), ⵢⵓⵛⵛⵍ ⴰⴷ ⵉⴳ x₁ = x₂. ⴰⵎⴷⵢⴰ: f(x) = 2x ⵜⴳⴰ ⵜⴰⵢⵏⴳⵉⵔⵜ.
   ⵜⴰⵙⵖⵏⵜ ⵜⴰⴼⵍⴳⵉⵔⵜ: ⵜⴳⴰ ⵜⵙⵖⵏⵜ f: X → Y ⵜⴰⴼⵍⴳⵉⵔⵜ (ⵏⵖ "ⵖⴼ") ⵉⴳ ⵜⴳⴰ ⵜⵓⴳⵏⴰ ⵏⵏⵙ ⵜⴰⵣⴷⴰⵖⵓⵍⵜ Y ⵙ ⵜⵉⵎⵎⴰⴷ. ⴰⵏⴰⵎⴽ ⵏⵏⵙ ⵎⴰⵙ ⴷ ⵉ ⴽⵓ ⴰⴼⵔⴷⵉⵙ y ⴳ Y, ⵉⵍⵍⴰ ⴰⵡⴷ ⵢⴰⵏ ⵓⴼⵔⴷⵉⵙ x ⴳ X ⵍⵍⵉ ⴳ ⵔⴰⴷ ⵢⵉⵍⵉ f(x) = y. ⴰⵎⴷⵢⴰ: f(x) = x³ ⵙⴳ ℝ ⵖⵔ ℝ ⵜⴳⴰ ⵜⴰⴼⵍⴳⵉⵔⵜ.
   ⵜⴰⵙⵖⵏⵜ ⵜⴰⵙⵏⴳⵉⵔⵜ: ⵜⴳⴰ ⵜⵙⵖⵏⵜ ⵜⴰⵙⵏⴳⵉⵔⵜ ⵉⴳ ⵜⴳⴰ ⵜⴰⵢⵏⴳⵉⵔⵜ ⴷ ⵜⴼⵍⴳⵉⵔⵜ ⴳ ⵢⴰⵏ ⵡⴰⴽⵓⴷ. ⴰⵏⴰⵎⴽ ⵏⵏⵙ ⵎⴰⵙ ⴷ ⴽⵓ ⴰⴼⵔⴷⵉⵙ ⴳ ⵜⴰⵖⵓⵍⵜ ⵉⵣⴷⵉ ⴷ ⵢⴰⵏ ⵓⴼⵔⴷⵉⵙ ⴰⵎⵢⵉⵡⵏ ⴳ ⵜⵣⴷⴰⵖⵓⵍⵜ, ⴷ ⴽⵓ ⴰⴼⵔⴷⵉⵙ ⴳ ⵜⵣⴷⴰⵖⵓⵍⵜ ⵉⵣⴷⵉ ⴷ ⵢⴰⵏ ⵓⴼⵔⴷⵉⵙ ⴰⵎⵢⵉⵡⵏ ⴳ ⵜⴰⵖⵓⵍⵜ. ⵜⵉⵙⵖⵏⵉⵏ ⵜⵉⵙⵏⴳⵉⵔⵉⵏ ⵖⵓⵔⵙⵏⵜ ⵜⵉⵙⵖⵏⵉⵏ ⵜⵉⵎⵙⴰⵖⵓⵍⵉⵏ. ⴰⵎⴷⵢⴰ: f(x) = x + 1 ⵜⴳⴰ ⵜⴰⵙⵏⴳⵉⵔⵜ ⵙⴳ ℝ ⵖⵔ ℝ.

 ⴰⵏⴰⵡⵏ ⵉⵜⵜⵓⵙⵙⴰⵏⵏ ⵏ ⵜⵙⵖⵏⵉⵏ 
   ⵜⵉⵙⵖⵏⵉⵏ ⵜⵉⴳⵜⴼⵓⵍⵉⵏ: ⵜⵜⵓⵚⴽⴰⵏⵜ ⵜⵙⵖⵏⵉⵏ ⴰⴷ ⵙⴳ ⵜⵎⵔⵏⵉⵡⵜ ⵏ ⵉⵏⴼⵙⴰⵔⵏ ⵓⵎⵎⵉⴷⵏ ⵓⵎⵏⵉⴳⵏ ⵏ ⵓⵎⵙⴽⵉⵍ. ⵜⴰⵍⵖⴰ ⵜⴰⵎⴰⵜⴰⵢⵜ ⵏⵏⵙⵏⵜ ⵜⴳⴰ .
   ⵜⵉⵙⵖⵏⵉⵏ ⵜⵉⵖⵥⵏⴰⵏⵉⵏ: ⵜⵉⴷ ⴳⴰⵏⵜ ⴰⵙⵙⴰⵖ ⵏ ⵙⵏⴰⵜ ⵜⵙⵖⵏⵉⵏ ⵜⵉⴳⵜⴼⵓⵍⵉⵏ, , ⵍⵍⵉ ⴳ .
   ⵜⵉⵙⵖⵏⵉⵏ ⵜⵉⴽⵕⴷⵉⵙⴽⵜⴰⵏⵉⵏ: ⵣⵓⵏ ⴷ , , ⴷ . ⵜⵉⵙⵖⵏⵉⵏ ⴰⴷ ⵜⵜⵓⵙⵎⵔⴰⵙⵏⵜ ⴱⴰⵀⵔⴰ ⴳ ⵓⴳⵍⴰⵎ ⵏ ⵜⵓⵎⴰⵏⵉⵏ ⵜⵉⵡⴰⵍⴰⵏⵉⵏ.
   ⵜⵉⵙⵖⵏⵉⵏ ⵜⵉⵙⵏⵏⴼⵙⴰⵔⵉⵏ: ⵜⵉⴷ ⵍⵍⴰⵏⵜ ⴳ ⵜⵍⵖⴰ , ⵍⵍⵉ ⴳ ⵜⴳⴰ ⵜⵙⵉⵍⴰ a ⵉⵎⵣⴳⵉ ⵓⵎⵏⵉⴳ. ⴰⵏⵏⵔⵏⵉ ⵏⵏⵙⵏⵜ ⵉⵎⵎⵔⵉⵏ ⵉⴳⴰ ⵢⴰⵏ ⵙⴳ ⵜⴼⵔⵉⵙⵉⵏ ⵏⵏⵙⵏⵜ ⵜⵉⵔⵙⵍⴰⵏⵉⵏ.
   ⵜⵉⵙⵖⵏⵉⵏ ⵜⵉⵍⵓⴳⴰⵔⵉⵜⵎⵉⵏ: ⵜⵉⴷ ⴳⴰⵏⵜ ⵜⵉⵙⵖⵏⵉⵏ ⵜⵉⵎⵙⴰⵖⵓⵍⵉⵏ ⵏ ⵜⵙⵖⵏⵉⵏ ⵜⵉⵙⵏⵏⴼⵙⴰⵔⵉⵏ. ⴷⴰ ⵜⵜⵓⵙⵎⵔⴰⵙⵏⵜ ⴳ ⵓⴼⵙⴰⵢ ⵏ ⵜⴳⴷⵉⵡⵉⵏ ⵍⵍⵉ ⴳ ⵉⵍⵍⴰ ⵓⵎⵙⴽⵉⵍ ⴳ ⵓⵏⴼⵙⴰⵔ.

 ⵉⵙⴰⵖⵓⵍⵏ 

ⴰⵙⵎⵉⵍ:ⵜⵉⵙⵖⵏⵉⵏ
ⴰⵙⵎⵉⵍ:ⵜⵉⵥⵕⵉ ⵏ ⵜⴳⵔⵓⵎⵎⵉⵡⵉⵏ