What is the g(x)=(6x^2+x-5)/(3x^2-7x-20) ?

The g(x)=(6x^2+x-5)/(3x^2-7x-20) is

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g(x)=(6x^2+x-5)/(3x^2-7x-20)

g (x) = \frac{6 x ^{2} + x - 5}{3 x ^{2} - 7 x - 20}

Domain : x < - \frac{5}{3} or - \frac{5}{3} < x < 4 or x > 4

Range : f (x) \leq \frac{- 30 38 + 263}{289} or f (x) \geq \frac{30 38 + 263}{289}

X Intercepts : (\frac{5}{6}, 0), (- 1, 0), Y Intercepts : (0, \frac{1}{4})

Asymptotes : Vertical x = - \frac{5}{3}, x = 4, Horizontal y = 2

Extreme Points : Minimum (- \frac{7 + 38}{3}, \frac{263 + 30 38}{289}), Maximum (- \frac{7 - 38}{3}, \frac{263 - 30 38}{289})

Interval Notation

Domain : (- \infty, - \frac{5}{3}) \cup (- \frac{5}{3}, 4) \cup (4, \infty)

Range : (- \infty, \frac{- 30 38 + 263}{289}] \cup [\frac{30 38 + 263}{289}, \infty)

Solution steps

Domain of

\frac{6 x ^{2} + x - 5}{3 x ^{2} - 7 x - 20} : x < - \frac{5}{3} or - \frac{5}{3} < x < 4 or x > 4

Range of

\frac{6 x ^{2} + x - 5}{3 x ^{2} - 7 x - 20} : f (x) \leq \frac{- 30 38 + 263}{289} or f (x) \geq \frac{30 38 + 263}{289}

Axis interception points of

\frac{6 x ^{2} + x - 5}{3 x ^{2} - 7 x - 20} :

X Intercepts

: (\frac{5}{6}, 0), (- 1, 0),

Y Intercepts

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

Asymptotes of

\frac{6 x ^{2} + x - 5}{3 x ^{2} - 7 x - 20} :

Vertical

: x = - \frac{5}{3}, x = 4,

Horizontal

: y = 2

Extreme Points of

\frac{6 x ^{2} + x - 5}{3 x ^{2} - 7 x - 20} :

Minimum

(- \frac{7 + 38}{3}, \frac{263 + 30 38}{289}),

Maximum

(- \frac{7 - 38}{3}, \frac{263 - 30 38}{289})