en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

f(x)=(3x^2+6)/(x^2-2x-3)

Solution

f (x) = \frac{3 x ^{2} + 6}{x ^{2} - 2 x - 3}

Solution

Domain : x < - 1 or - 1 < x < 3 or x > 3

Range : f (x) \leq \frac{- 3 33 + 3}{8} or f (x) \geq \frac{3 33 + 3}{8}

Y Intercepts : (0, - 2)

Asymptotes : Vertical x = - 1, x = 3, Horizontal y = 3

Extreme Points : Minimum (- \frac{5 + 33}{2}, \frac{3 ( 1 + 33 )}{8}), Maximum (\frac{33 - 5}{2}, - \frac{3 ( 33 - 1 )}{8})

+1

Interval Notation

Domain : (- \infty, - 1) \cup (- 1, 3) \cup (3, \infty)

Range : (- \infty, \frac{- 3 33 + 3}{8}] \cup [\frac{3 33 + 3}{8}, \infty)

Solution steps

Domain of

\frac{3 x ^{2} + 6}{x ^{2} - 2 x - 3} : x < - 1 or - 1 < x < 3 or x > 3

Range of

\frac{3 x ^{2} + 6}{x ^{2} - 2 x - 3} : f (x) \leq \frac{- 3 33 + 3}{8} or f (x) \geq \frac{3 33 + 3}{8}

Axis interception points of

\frac{3 x ^{2} + 6}{x ^{2} - 2 x - 3} :

Y Intercepts

: (0, - 2)

Asymptotes of

\frac{3 x ^{2} + 6}{x ^{2} - 2 x - 3} :

Vertical

: x = - 1, x = 3,

Horizontal

: y = 3

Extreme Points of

\frac{3 x ^{2} + 6}{x ^{2} - 2 x - 3} :

Minimum

(- \frac{5 + 33}{2}, \frac{3 ( 1 + 33 )}{8}),

Maximum

(\frac{33 - 5}{2}, - \frac{3 ( 33 - 1 )}{8})

Popular Examples

f(x)=(x+5)(x-3)^2

f (x) = (x + 5) (x - 3)^{2}

f (y) = y^{2} - 4 y - 3

f (x) = x^{4} - 3 x + 1

y= 2/3 x^{3/2},0<= x<= 1

y = \frac{2}{3} x^{\frac{3}{2}}, 0 \leq x \leq 1

f(x)=3+log_{3}(x+2)

f (x) = 3 + lo g_{3} (x + 2)

Frequently Asked Questions (FAQ)

What is the f(x)=(3x^2+6)/(x^2-2x-3) ?
The f(x)=(3x^2+6)/(x^2-2x-3) is