What is the f(x)=(x^2+7x)/(x^3-5x^2-14x) ?

The f(x)=(x^2+7x)/(x^3-5x^2-14x) is

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f(x)=(x^2+7x)/(x^3-5x^2-14x)

f (x) = \frac{x ^{2} + 7 x}{x ^{3} - 5 x ^{2} - 14 x}

Domain : x < - 2 or - 2 < x < 0 or 0 < x < 7 or x > 7

Range : f (x) \leq - \frac{2 70 + 19}{81} or f (x) \geq - \frac{19 - 2 70}{81}

X Intercepts : (- 7, 0)

Asymptotes : Vertical x = - 2, x = 7, Horizontal y = 0

Extreme Points : Minimum (- 7 - 70, - \frac{19 - 2 70}{81}), Maximum (- 7 + 70, - \frac{2 70 + 19}{81})

Interval Notation

Domain : (- \infty, - 2) \cup (- 2, 0) \cup (0, 7) \cup (7, \infty)

Range : (- \infty, - \frac{2 70 + 19}{81}] \cup [- \frac{19 - 2 70}{81}, \infty)

Solution steps

Domain of

\frac{x ^{2} + 7 x}{x ^{3} - 5 x ^{2} - 14 x} : x < - 2 or - 2 < x < 0 or 0 < x < 7 or x > 7

Range of

\frac{x ^{2} + 7 x}{x ^{3} - 5 x ^{2} - 14 x} : f (x) \leq - \frac{2 70 + 19}{81} or f (x) \geq - \frac{19 - 2 70}{81}

Axis interception points of

\frac{x ^{2} + 7 x}{x ^{3} - 5 x ^{2} - 14 x} :

X Intercepts

: (- 7, 0)

Asymptotes of

\frac{x ^{2} + 7 x}{x ^{3} - 5 x ^{2} - 14 x} :

Vertical

: x = - 2, x = 7,

Horizontal

: y = 0

Extreme Points of

\frac{x ^{2} + 7 x}{x ^{3} - 5 x ^{2} - 14 x} :

Minimum

(- 7 - 70, - \frac{19 - 2 70}{81}),

Maximum

(- 7 + 70, - \frac{2 70 + 19}{81})

y = cos^{3} (2 x + \frac{π}{2})

f (x) = - 8 + \frac{1}{2} x

y = - 2 x^{2} + 8 x - 14

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