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 x ⵙ ⵓⵎⴽⴽⵓⵥ ⵏⵏⵙ x^2 ⵜⴳⴰ ⵜⴰⵙⵖⵏⵜ.

## ⴰⵙⵏⵎⵍ ⴰⵍⵖⴰⵏ
thumb|ⵓⵏⵓⵖ ⵉⵜⵜⴳⵍⴰⵎⵏ ⵜⴰⵙⵖⵏⵜ ⴰⵎⵎ ⵢⴰⵜ ⵜⵎⴰⵛⵉⵏⵜ ⵏⵖ ⵜⴰⴼⵏⵉQT ⵢⴰⴽⴽⴰⵏ ⵉ ⴽⵓ ⵜⴰⵏⴽⵛⵓⵎⵜ ⵜⵓⴼⴼⵖⴰ ⵏⵏⵙ.
thumb|ⴰⵎⴽⵏⴰⵡ ⴰⵣⴳⴳⵯⴰⵖ ⵉⴳⴰ ⴰⵎⵙⴽⴰⵏ ⵏ ⵜⵙⵖⵏⵜ, ⴰⵛⴽⵓ ⴽⵓ ⴰⵣⵔⵉⴳ ⴰⴱⴷⴷⴰⵢ ⴷⴰⵔⵙ ⵖⴰⵙ ⵢⴰⵏ ⵜⵇⵉⴼⵉⵜ ⵏ ⵓⵎⵢⴰⴱⴰⵢ ⴰⴽⴷ ⵓⵎⴽⵏⴰⵡ.

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

thumb|ⴰⵎⵙⴽⴰⵏ ⵏ ⵢⴰⵜ ⵜⵙⵖⵏⵜ
thumb|ⴰⵎⵙⴽⴰⵏ ⵏ ⵜⵓⵇⵇⵏⴰ ⵓⵔ ⵉⴳⵉⵏ ⵜⴰⵙⵖⵏⵜ. ⵢⴰⵏ ⵙ ⵉⵙⵔⴰⴳⵏ ⵏ ⵓⵢⴰⵏⵏ ⵉⴳⴰ ⵜ ⵎⴰⵙ 2 ⵉⴳⴰ ⴰⴼⵔⴷⵉⵙ ⴰⵎⵣⵡⴰⵔⵓ ⴳ ⵡⵓⴳⴳⴰⵔ ⵏ ⵜⵢⵓⴳⴰ ⵉⵏⵎⴰⵍⴰⵏ. ⴷ ⵓⵙⵔⴰⴳ ⵢⴰⴹⵏⵉⵏ ⵉⴳⴰ ⵜ ⵎⴰⵙ ⴷ 3 ⴷ 4 ⵓⵔ ⴳⵉⵏ ⴰⴼⵔⴷⵉⵙ ⴰⵎⵣⵡⴰⵔⵓ (ⴰⵏⴽⵛⵓⵎ) ⴳ ⴽⵔⴰ ⵏ ⵜⵢⵓⴳⴰ ⵉⵏⵎⴰⵍⴰⵏ.

ⵜⴻⵜⵜⵓⵙⵎⵎⴰ ⵜⴳⵔⵓⵎⵎⴰ ⵏ ⵡⴰⵣⴰⵍⵏ ⴰⴽⴽⵯ f(x) ⵍⵍⵉ ⵏⵥⴹⴰⵕ ⴰⴷ ⵏⴰⴼ ⵜⵓⴳⵏⴰ ⵏ ⵜⵙⵖⵏⵜ f ⵏⵖ ⴰⵣⵉⵍⴰⵍ ⵏⵏⵙ. ⵉⵇⵇⴰⵏ ⴷ ⴰⴷ ⵓⵔ ⵏⵙⵎⵔⴽⴰⵙ ⴳⵔ ⵜⵓⴳⵏⴰ (ⴰⵣⵉⵍⴰⵍ) ⴷ ⵜⵣⴷⴰⵖⵓⵍⵜ. ⵜⴰⵣⴷⴰⵖⵓⵍⵜ ⵜⴳⴰ ⵜⴰⴳⵔⵓⵎⵎⴰ Y 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 f(x) = x^2, ⵉⴳ ⵜⴳⴰ ⵜⴰⵖⵓⵍⵜ ⴷ ⵜⵣⴷⴰⵖⵓⵍⵜ ⵜⴳⵔⵓⵎⵎⴰ ⵏ ⵉⵎⴹⴰⵏⵏ ⵉⵏⵉⵍⴰⵡⵏ \mathbb{R}, ⵀⴰⵜ ⴰⵣⵉⵍⴰⵍ (ⵜⵓⴳⵏⴰ) ⵉⴳⴰ ⵜⴰⴳⵔⵓⵎⵎⴰ ⵏ ⵉⵎⴹⴰⵏⵏ ⵉⵏⵉⵍⴰⵡⵏ ⵓⵎⵏⵉⴳⵏ [0, +\infty), 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* ↦ *x*².

## 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*) = 3*x*² - 4*x* + 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 (*e*ˣ), 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 f(x) = x^2, ⵜⴰⴼⵍⵡⵉⵜ ⵔⴰⴷ ⵜⴳ ⵉⵎⴽⴰ:

ⵜⴰⴼⵍⵡⵉⵜ ⵏ ⵡⴰⵣⴰⵍⵏ ⵉ:  f(x) = x^2

## 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*) = 2*x* 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*) = *x*³ 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 f(x) = a_n x^n + a_{n-1} x^{n-1} + \dots + a_1 x + a_0.
*   **ⵜⵉⵙⵖⵏⵉⵏ ⵜⵉⵖⵥⵏⴰⵏⵉⵏ**: ⵜⵉⴷ ⴳⴰⵏⵜ ⴰⵙⵙⴰⵖ ⵏ ⵙⵏⴰⵜ ⵜⵙⵖⵏⵉⵏ ⵜⵉⴳⵜⴼⵓⵍⵉⵏ, f(x) = P(x) / Q(x), ⵍⵍⵉ ⴳ Q(x) \neq 0.
*   **ⵜⵉⵙⵖⵏⵉⵏ ⵜⵉⴽⵕⴷⵉⵙⴽⵜⴰⵏⵉⵏ**: ⵣⵓⵏ ⴷ sin(x), cos(x), ⴷ tan(x). ⵜⵉⵙⵖⵏⵉⵏ ⴰⴷ ⵜⵜⵓⵙⵎⵔⴰⵙⵏⵜ ⴱⴰⵀⵔⴰ ⴳ ⵓⴳⵍⴰⵎ ⵏ ⵜⵓⵎⴰⵏⵉⵏ ⵜⵉⵡⴰⵍⴰⵏⵉⵏ.
*   **ⵜⵉⵙⵖⵏⵉⵏ ⵜⵉⵙⵏⵏⴼⵙⴰⵔⵉⵏ**: ⵜⵉⴷ ⵍⵍⴰⵏⵜ ⴳ ⵜⵍⵖⴰ f(x) = a^x, 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