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Popular >

y=(21x^2+16x+3)/(21x^2-x-2)

Solution

y = \frac{21 x ^{2} + 16 x + 3}{21 x ^{2} - x - 2}

Solution

Domain : x < - \frac{2}{7} or - \frac{2}{7} < x < \frac{1}{3} or x > \frac{1}{3}

Range : f (x) \leq \frac{- 8 42 - 58}{169} or f (x) \geq \frac{8 42 - 58}{169}

X Intercepts : (- \frac{1}{3}, 0), (- \frac{3}{7}, 0), Y Intercepts : (0, - \frac{3}{2})

Asymptotes : Vertical x = - \frac{2}{7}, x = \frac{1}{3}, Horizontal y = 1

Extreme Points : Minimum (- \frac{105 + 4 42}{357}, - \frac{2 ( 29 - 4 42 )}{169}), Maximum (- \frac{105 - 4 42}{357}, - \frac{2 ( 29 + 4 42 )}{169})

+1

Interval Notation

Domain : (- \infty, - \frac{2}{7}) \cup (- \frac{2}{7}, \frac{1}{3}) \cup (\frac{1}{3}, \infty)

Range : (- \infty, \frac{- 8 42 - 58}{169}] \cup [\frac{8 42 - 58}{169}, \infty)

Solution steps

Domain of

\frac{21 x ^{2} + 16 x + 3}{21 x ^{2} - x - 2} : x < - \frac{2}{7} or - \frac{2}{7} < x < \frac{1}{3} or x > \frac{1}{3}

Range of

\frac{21 x ^{2} + 16 x + 3}{21 x ^{2} - x - 2} : f (x) \leq \frac{- 8 42 - 58}{169} or f (x) \geq \frac{8 42 - 58}{169}

Axis interception points of

\frac{21 x ^{2} + 16 x + 3}{21 x ^{2} - x - 2} :

X Intercepts

: (- \frac{1}{3}, 0), (- \frac{3}{7}, 0),

Y Intercepts

: (0, - \frac{3}{2})

Asymptotes of

\frac{21 x ^{2} + 16 x + 3}{21 x ^{2} - x - 2} :

Vertical

: x = - \frac{2}{7}, x = \frac{1}{3},

Horizontal

: y = 1

Extreme Points of

\frac{21 x ^{2} + 16 x + 3}{21 x ^{2} - x - 2} :

Minimum

(- \frac{105 + 4 42}{357}, - \frac{2 ( 29 - 4 42 )}{169}),

Maximum

(- \frac{105 - 4 42}{357}, - \frac{2 ( 29 + 4 42 )}{169})

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Frequently Asked Questions (FAQ)

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