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Popular Functions >

f(x)=(x^4-x^3-8)/(x^2-x-6)

Solution

f (x) = \frac{x ^{4} - x ^{3} - 8}{x ^{2} - x - 6}

Solution

Domain : x < - 2 or - 2 < x < 3 or x > 3

Range : f (x) \leq 1.55233 \dots or f (x) \geq 16.22893 \dots

X Intercepts : (2, 0), (- 1.47796 \dots, 0), Y Intercepts : (0, \frac{4}{3})

Asymptotes : Vertical x = - 2, x = 3

Extreme Points : Minimum (- 2.74481 \dots, 16.22893 \dots), Maximum (- 0.80719 \dots, 1.55233 \dots), Minimum (0.41107 \dots, 1.28817 \dots), Maximum (1.08202 \dots, 1.33577 \dots), Minimum (4.05890 \dots, 30.63478 \dots)

+1

Interval Notation

Domain : (- \infty, - 2) \cup (- 2, 3) \cup (3, \infty)

Range : (- \infty, 1.55233 \dots] \cup [16.22893 \dots, \infty)

Solution steps

Domain of

\frac{x ^{4} - x ^{3} - 8}{x ^{2} - x - 6} : x < - 2 or - 2 < x < 3 or x > 3

Range of

\frac{x ^{4} - x ^{3} - 8}{x ^{2} - x - 6} : f (x) \leq 1.55233 \dots or f (x) \geq 16.22893 \dots

Axis interception points of

\frac{x ^{4} - x ^{3} - 8}{x ^{2} - x - 6} :

X Intercepts

: (2, 0), (- 1.47796 \dots, 0),

Y Intercepts

: (0, \frac{4}{3})

Asymptotes of

\frac{x ^{4} - x ^{3} - 8}{x ^{2} - x - 6} :

Vertical

: x = - 2, x = 3

Extreme Points of

\frac{x ^{4} - x ^{3} - 8}{x ^{2} - x - 6} :

Minimum

(- 2.74481 \dots, 16.22893 \dots),

Maximum

(- 0.80719 \dots, 1.55233 \dots),

Minimum

(0.41107 \dots, 1.28817 \dots),

Maximum

(1.08202 \dots, 1.33577 \dots),

Minimum

(4.05890 \dots, 30.63478 \dots)

Graph

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Frequently Asked Questions (FAQ)

What is the f(x)=(x^4-x^3-8)/(x^2-x-6) ?
The f(x)=(x^4-x^3-8)/(x^2-x-6) is