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Popular >

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

Solution

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

Solution

Domain : x < - 2 or - 2 < x < 2 or x > 2

Range : f (x) \leq \frac{- 13 - 9}{8} or f (x) \geq \frac{13 - 9}{8}

X Intercepts : (- \frac{3 + 17}{4}, 0), (\frac{17 - 3}{4}, 0), Y Intercepts : (0, - \frac{1}{4})

Asymptotes : Vertical x = - 2, x = 2, Horizontal y = - 2

Extreme Points : Maximum (- \frac{7 + 13}{3}, - \frac{9 + 13}{8}), Minimum (\frac{- 7 + 13}{3}, - \frac{9 - 13}{8})

+1

Interval Notation

Domain : (- \infty, - 2) \cup (- 2, 2) \cup (2, \infty)

Range : (- \infty, \frac{- 13 - 9}{8}] \cup [\frac{13 - 9}{8}, \infty)

Solution steps

Domain of

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

Range of

\frac{- 2 x ^{2} - 3 x + 1}{x ^{2} - 4} : f (x) \leq \frac{- 13 - 9}{8} or f (x) \geq \frac{13 - 9}{8}

Axis interception points of

\frac{- 2 x ^{2} - 3 x + 1}{x ^{2} - 4} :

X Intercepts

: (- \frac{3 + 17}{4}, 0), (\frac{17 - 3}{4}, 0),

Y Intercepts

: (0, - \frac{1}{4})

Asymptotes of

\frac{- 2 x ^{2} - 3 x + 1}{x ^{2} - 4} :

Vertical

: x = - 2, x = 2,

Horizontal

: y = - 2

Extreme Points of

\frac{- 2 x ^{2} - 3 x + 1}{x ^{2} - 4} :

Maximum

(- \frac{7 + 13}{3}, - \frac{9 + 13}{8}),

Minimum

(\frac{- 7 + 13}{3}, - \frac{9 - 13}{8})

Popular Examples

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Frequently Asked Questions (FAQ)

What is the f(x)=(-2x^2-3x+1)/(x^2-4) ?
The f(x)=(-2x^2-3x+1)/(x^2-4) is