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Popular >

f(x)=(2x^2+2x-9)/(3x^2-5)

Solution

f (x) = \frac{2 x ^{2} + 2 x - 9}{3 x ^{2} - 5}

Solution

Domain : x < - \frac{5}{3} or - \frac{5}{3} < x < \frac{5}{3} or x > \frac{5}{3}

Range : f (x) \leq \frac{- 229 + 37}{30} or f (x) \geq \frac{229 + 37}{30}

X Intercepts : (\frac{- 1 + 19}{2}, 0), (- \frac{1 + 19}{2}, 0), Y Intercepts : (0, \frac{9}{5})

Asymptotes : Vertical x = - \frac{5}{3}, x = \frac{5}{3}, Horizontal y = \frac{2}{3}

Extreme Points : Minimum (\frac{17 - 229}{6}, \frac{37 + 229}{30}), Maximum (\frac{17 + 229}{6}, \frac{37 - 229}{30})

+1

Interval Notation

Domain : (- \infty, - \frac{5}{3}) \cup (- \frac{5}{3}, \frac{5}{3}) \cup (\frac{5}{3}, \infty)

Range : (- \infty, \frac{- 229 + 37}{30}] \cup [\frac{229 + 37}{30}, \infty)

Solution steps

Domain of

\frac{2 x ^{2} + 2 x - 9}{3 x ^{2} - 5} : x < - \frac{5}{3} or - \frac{5}{3} < x < \frac{5}{3} or x > \frac{5}{3}

Range of

\frac{2 x ^{2} + 2 x - 9}{3 x ^{2} - 5} : f (x) \leq \frac{- 229 + 37}{30} or f (x) \geq \frac{229 + 37}{30}

Axis interception points of

\frac{2 x ^{2} + 2 x - 9}{3 x ^{2} - 5} :

X Intercepts

: (\frac{- 1 + 19}{2}, 0), (- \frac{1 + 19}{2}, 0),

Y Intercepts

: (0, \frac{9}{5})

Asymptotes of

\frac{2 x ^{2} + 2 x - 9}{3 x ^{2} - 5} :

Vertical

: x = - \frac{5}{3}, x = \frac{5}{3},

Horizontal

: y = \frac{2}{3}

Extreme Points of

\frac{2 x ^{2} + 2 x - 9}{3 x ^{2} - 5} :

Minimum

(\frac{17 - 229}{6}, \frac{37 + 229}{30}),

Maximum

(\frac{17 + 229}{6}, \frac{37 - 229}{30})

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Frequently Asked Questions (FAQ)

What is the f(x)=(2x^2+2x-9)/(3x^2-5) ?
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