en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y=(2x^2+2x+3)/(4x^2-4x)

Solution

y = \frac{2 x ^{2} + 2 x + 3}{4 x ^{2} - 4 x}

Solution

Domain : x < 0 or 0 < x < 1 or x > 1

Range : f (x) \leq - \frac{21}{2} - 2 or f (x) \geq \frac{21}{2} - 2

Intercepts : None

Asymptotes : Vertical x = 0, x = 1, Horizontal y = \frac{1}{2}

Extreme Points : Minimum (- \frac{3 + 21}{4}, \frac{21 - 4}{2}), Maximum (\frac{- 3 + 21}{4}, - \frac{4 + 21}{2})

+1

Interval Notation

Domain : (- \infty, 0) \cup (0, 1) \cup (1, \infty)

Range : (- \infty, - \frac{21}{2} - 2] \cup [\frac{21}{2} - 2, \infty)

Solution steps

Domain of

\frac{2 x ^{2} + 2 x + 3}{4 x ^{2} - 4 x} : x < 0 or 0 < x < 1 or x > 1

Range of

\frac{2 x ^{2} + 2 x + 3}{4 x ^{2} - 4 x} : f (x) \leq - \frac{21}{2} - 2 or f (x) \geq \frac{21}{2} - 2

Axis interception points of

\frac{2 x ^{2} + 2 x + 3}{4 x ^{2} - 4 x} :

None

Asymptotes of

\frac{2 x ^{2} + 2 x + 3}{4 x ^{2} - 4 x} :

Vertical

: x = 0, x = 1,

Horizontal

: y = \frac{1}{2}

Extreme Points of

\frac{2 x ^{2} + 2 x + 3}{4 x ^{2} - 4 x} :

Minimum

(- \frac{3 + 21}{4}, \frac{21 - 4}{2}),

Maximum

(\frac{- 3 + 21}{4}, - \frac{4 + 21}{2})

Popular Examples

f (x) = \frac{x ^{4}}{2}

y = x^{3} - 3 x^{2} - 1

f (x) = \frac{1}{2 x + 4}

f (x) = 2 x^{3} - x + 4

f(x)=(x+4/3)(x+1/2)

f (x) = (x + \frac{4}{3}) (x + \frac{1}{2})

Frequently Asked Questions (FAQ)

What is the y=(2x^2+2x+3)/(4x^2-4x) ?
The y=(2x^2+2x+3)/(4x^2-4x) is