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Popular >

g(x)=(x^2+8x+15)/(x^2-81)

Solution

g (x) = \frac{x ^{2} + 8 x + 15}{x ^{2} - 81}

Solution

Domain : x < - 9 or - 9 < x < 9 or x > 9

Range : f (x) \leq \frac{- 4 7 + 11}{27} or f (x) \geq \frac{4 7 + 11}{27}

X Intercepts : (- 3, 0), (- 5, 0), Y Intercepts : (0, - \frac{5}{27})

Asymptotes : Vertical x = - 9, x = 9, Horizontal y = 1

Extreme Points : Minimum (- 3 (4 + 7), \frac{11 + 4 7}{27}), Maximum (- 3 (4 - 7), \frac{11 - 4 7}{27})

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Solution steps

Domain of

\frac{x ^{2} + 8 x + 15}{x ^{2} - 81} : x < - 9 or - 9 < x < 9 or x > 9

Range of

\frac{x ^{2} + 8 x + 15}{x ^{2} - 81} : f (x) \leq \frac{- 4 7 + 11}{27} or f (x) \geq \frac{4 7 + 11}{27}

Axis interception points of

\frac{x ^{2} + 8 x + 15}{x ^{2} - 81} :

X Intercepts

: (- 3, 0), (- 5, 0),

Y Intercepts

: (0, - \frac{5}{27})

Asymptotes of

\frac{x ^{2} + 8 x + 15}{x ^{2} - 81} :

Vertical

: x = - 9, x = 9,

Horizontal

: y = 1

Extreme Points of

\frac{x ^{2} + 8 x + 15}{x ^{2} - 81} :

Minimum

(- 3 (4 + 7), \frac{11 + 4 7}{27}),

Maximum

(- 3 (4 - 7), \frac{11 - 4 7}{27})

Popular Examples

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y = 2 x^{2} + 3 x + 2

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

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

f(x)=-3(x-5)^2-1

f (x) = - 3 (x - 5)^{2} - 1

Frequently Asked Questions (FAQ)

What is the g(x)=(x^2+8x+15)/(x^2-81) ?
The g(x)=(x^2+8x+15)/(x^2-81) is