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Popular >

f(x)=((2x+1)(x-5))/(3x+2)

Solution

f (x) = \frac{( 2 x + 1 ) ( x - 5 )}{3 x + 2}

Solution

Domain : x < - \frac{2}{3} or x > - \frac{2}{3}

Range : f (x) \leq \frac{- 2 34 - 35}{9} or f (x) \geq \frac{2 34 - 35}{9}

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

Asymptotes : Vertical x = - \frac{2}{3}, Slant y = \frac{2}{3} x - \frac{31}{9}

Extreme Points : Maximum (- \frac{4 + 34}{6}, \frac{- 34 2 - 35 17}{9 17}), Minimum (\frac{- 4 + 34}{6}, \frac{34 2 - 35 17}{9 17})

+1

Interval Notation

Domain : (- \infty, - \frac{2}{3}) \cup (- \frac{2}{3}, \infty)

Range : (- \infty, \frac{- 2 34 - 35}{9}] \cup [\frac{2 34 - 35}{9}, \infty)

Solution steps

Domain of

\frac{( 2 x + 1 ) ( x - 5 )}{3 x + 2} : x < - \frac{2}{3} or x > - \frac{2}{3}

Range of

\frac{( 2 x + 1 ) ( x - 5 )}{3 x + 2} : f (x) \leq \frac{- 2 34 - 35}{9} or f (x) \geq \frac{2 34 - 35}{9}

Axis interception points of

\frac{( 2 x + 1 ) ( x - 5 )}{3 x + 2} :

X Intercepts

: (- \frac{1}{2}, 0), (5, 0),

Y Intercepts

: (0, - \frac{5}{2})

Asymptotes of

\frac{( 2 x + 1 ) ( x - 5 )}{3 x + 2} :

Vertical

: x = - \frac{2}{3},

Slant

: y = \frac{2}{3} x - \frac{31}{9}

Extreme Points of

\frac{( 2 x + 1 ) ( x - 5 )}{3 x + 2} :

Maximum

(- \frac{4 + 34}{6}, \frac{- 34 2 - 35 17}{9 17}),

Minimum

(\frac{- 4 + 34}{6}, \frac{34 2 - 35 17}{9 17})

Popular Examples

f (x) = x^{2} - 3 x - 6

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f (x) = - x + 9

f (x) = 2 x^{3} + 5

f (x) = 10 - x

Frequently Asked Questions (FAQ)

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