Fungsi

Domain dan Range

DOMAIN NATURAL

$$f(x) = \dfrac 1x$$

$$x > 0$$

$$f(x) = \sqrt{x}$$

$$x \geq 0$$

$$f(x) = \: ^a \log x$$

$$a > 0 \text{ dan } x > 0$$

DOMAIN DAN RANGE BEBERAPA FUNGSI KHUSUS
A. Fungsi Linear
$$y = mx + c$$

Domain

$$- \sim \: < x < \: \sim$$

Range

$$- \sim \: < y < \: \sim$$

Kurva membuka ke atas

$$y = ax^2 + bx + c, \: a > 0$$

Domain

$$- \sim \: < x < \: \sim$$

Range

$$\{y \geq y_{\text{min}}\}$$

Menentukan x puncak

$$x_{\text{puncak}} = - \dfrac {b}{2a}$$

Menentukan y puncak

Substitusi nilai $$x_{\text{puncak}}$$ ke dalam persamaan fungsi untuk mendapatkan nilai y

Kurva membuka ke bawah

$$y = ax^2 + bx + c, \: a < 0$$

Domain

$$- \sim \: < x < \: \sim$$

Range

$$\{y \leq y_{\text{max}}\}$$

C. Fungsi Akar
$$y = \sqrt{x}$$

Domain

$$x \geq 0$$

Range

$$y \geq 0$$

D. Fungsi Eksponen
$$y = a^x$$

Domain

$$\{x \in R\}$$

Range

$$\{y > 0\}$$

Asymtote:

$$y = 0$$

E. Fungsi Logaritma
$$y = \log x$$

Domain

$$x > 0$$

Range

$$\{y \in R\}$$

Asymtote:

$$x = 0$$

F. Fungsi Pecahan
$$y = \dfrac 1x$$

Asymtote datar

$$y = 0$$

Asymtote tegak

$$x = 0$$

Domain

$$\{x \neq 0\}$$

Range

$$\{y \neq 0\}$$

G. Fungsi Pecahan
$$y = \dfrac {ax + b}{cx + d}$$

Asymtote datar

$$y = \dfrac ac$$

Asymtote tegak

$$cx + d = 0$$

$$x = - \dfrac dc$$

Domain

$$\{x \neq \text{ asymtote tegak}\}$$

Range

$$\{y \neq \text{ asymtote datar}\}$$

SOAL LATIHAN

--- Khusus Member ---