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Beliebt Rechnen >

f(x)=(-4x^2+3x-7)/(2x^2-10x-3)

Lösung

f (x) = \frac{- 4 x ^{2} + 3 x - 7}{2 x ^{2} - 10 x - 3}

Lösung

Domain : x < \frac{5 - 31}{2} or \frac{5 - 31}{2} < x < \frac{5 + 31}{2} or x > \frac{5 + 31}{2}

Range : f (x) \leq - \frac{41}{31 2} - \frac{13}{62} or f (x) \geq \frac{41}{31 2} - \frac{13}{62}

Y - Schnittpunkte : (0, \frac{7}{3})

Asymptotes : Vertikal x = \frac{5 - 31}{2}, x = \frac{5 + 31}{2}, Horizontal y = - 2

Extreme Points : Maximum (- \frac{26 + 41 2}{34}, - \frac{13 + 41 2}{62}), Minimum (\frac{- 26 + 41 2}{34}, \frac{41 2 - 13}{62})

+1

Intervall-Notation

Domain : (- \infty, \frac{5 - 31}{2}) \cup (\frac{5 - 31}{2}, \frac{5 + 31}{2}) \cup (\frac{5 + 31}{2}, \infty)

Range : (- \infty, - \frac{41}{31 2} - \frac{13}{62}] \cup [\frac{41}{31 2} - \frac{13}{62}, \infty)

Schritte zur Lösung

Bereich von

\frac{- 4 x ^{2} + 3 x - 7}{2 x ^{2} - 10 x - 3} : x < \frac{5 - 31}{2} or \frac{5 - 31}{2} < x < \frac{5 + 31}{2} or x > \frac{5 + 31}{2}

Bereich von

\frac{- 4 x ^{2} + 3 x - 7}{2 x ^{2} - 10 x - 3} : f (x) \leq - \frac{41}{31 2} - \frac{13}{62} or f (x) \geq \frac{41}{31 2} - \frac{13}{62}

Schnittpunkte mit der Achse von

\frac{- 4 x ^{2} + 3 x - 7}{2 x ^{2} - 10 x - 3} :

Y-Schnittpunkte

: (0, \frac{7}{3})

Asymptoten von

\frac{- 4 x ^{2} + 3 x - 7}{2 x ^{2} - 10 x - 3} :

Vertikal

: x = \frac{5 - 31}{2}, x = \frac{5 + 31}{2},

Horizontal

: y = - 2

Extrempunkte vonf

\frac{- 4 x ^{2} + 3 x - 7}{2 x ^{2} - 10 x - 3} :

Maximum

(- \frac{26 + 41 2}{34}, - \frac{13 + 41 2}{62}),

Minimum

(\frac{- 26 + 41 2}{34}, \frac{41 2 - 13}{62})

Graph

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