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Popular >

y=(2x^2-3x+1)/(2x^2+8x+6)

Solution

y = \frac{2 x ^{2} - 3 x + 1}{2 x ^{2} + 8 x + 6}

Solution

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

Range : f (x) \leq - \frac{21}{2} - \frac{13}{4} or f (x) \geq \frac{21}{2} - \frac{13}{4}

X Intercepts : (1, 0), (\frac{1}{2}, 0), Y Intercepts : (0, \frac{1}{6})

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

Extreme Points : Maximum (- \frac{5 + 2 42}{11}, - \frac{13 + 2 42}{4}), Minimum (\frac{- 5 + 2 42}{11}, - \frac{13 - 2 42}{4})

+1

Interval Notation

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

Range : (- \infty, - \frac{21}{2} - \frac{13}{4}] \cup [\frac{21}{2} - \frac{13}{4}, \infty)

Solution steps

Domain of

\frac{2 x ^{2} - 3 x + 1}{2 x ^{2} + 8 x + 6} : x < - 3 or - 3 < x < - 1 or x > - 1

Range of

\frac{2 x ^{2} - 3 x + 1}{2 x ^{2} + 8 x + 6} : f (x) \leq - \frac{21}{2} - \frac{13}{4} or f (x) \geq \frac{21}{2} - \frac{13}{4}

Axis interception points of

\frac{2 x ^{2} - 3 x + 1}{2 x ^{2} + 8 x + 6} :

X Intercepts

: (1, 0), (\frac{1}{2}, 0),

Y Intercepts

: (0, \frac{1}{6})

Asymptotes of

\frac{2 x ^{2} - 3 x + 1}{2 x ^{2} + 8 x + 6} :

Vertical

: x = - 3, x = - 1,

Horizontal

: y = 1

Extreme Points of

\frac{2 x ^{2} - 3 x + 1}{2 x ^{2} + 8 x + 6} :

Maximum

(- \frac{5 + 2 42}{11}, - \frac{13 + 2 42}{4}),

Minimum

(\frac{- 5 + 2 42}{11}, - \frac{13 - 2 42}{4})

Popular Examples

y=-0.0556x^2+1.6661x-0.1612

y = - 0.0556 x^{2} + 1.6661 x - 0.1612

f(x)=(x^4}{12}+\frac{x^3)/6-x^2+x

f (x) = \frac{x ^{4}}{12} + \frac{x ^{3}}{6} - x^{2} + x

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

y = - 2 (x + 3) (x - 2)

f(x)=(x+6)/(x^2-9x+18)

f (x) = \frac{x + 6}{x ^{2} - 9 x + 18}

Frequently Asked Questions (FAQ)

What is the y=(2x^2-3x+1)/(2x^2+8x+6) ?
The y=(2x^2-3x+1)/(2x^2+8x+6) is