What is the f(x)=((x-1))/(x^3+6x^2+2x-4) ?

The f(x)=((x-1))/(x^3+6x^2+2x-4) is

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f(x)=((x-1))/(x^3+6x^2+2x-4)

f (x) = \frac{( x - 1 )}{x ^{3} + 6 x ^{2} + 2 x - 4}

Domain : x < - 5.50466 \dots or - 5.50466 \dots < x < - 1.13535 \dots or - 1.13535 \dots < x < 0.64002 \dots or x > 0.64002 \dots

Range : - \infty < f (x) < \infty

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

Asymptotes : Vertical x = - 5.50466 \dots, x = - 1.13535 \dots, x = 0.64002 \dots, Horizontal y = 0

Extreme Points : Maximum (- 3.36903 \dots, - 0.22845 \dots), Minimum (0.17524 \dots, 0.23837 \dots), Maximum (1.69378 \dots, 0.03232 \dots)

Solution steps

Domain of

\frac{x - 1}{x ^{3} + 6 x ^{2} + 2 x - 4} : x < - 5.50466 \dots or - 5.50466 \dots < x < - 1.13535 \dots or - 1.13535 \dots < x < 0.64002 \dots or x > 0.64002 \dots

Range of

\frac{x - 1}{x ^{3} + 6 x ^{2} + 2 x - 4} : - \infty < f (x) < \infty

Axis interception points of

\frac{x - 1}{x ^{3} + 6 x ^{2} + 2 x - 4} :

X Intercepts

: (1, 0),

Y Intercepts

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

Asymptotes of

\frac{x - 1}{x ^{3} + 6 x ^{2} + 2 x - 4} :

Vertical

: x = - 5.50466 \dots, x = - 1.13535 \dots, x = 0.64002 \dots,

Horizontal

: y = 0

Extreme Points of

\frac{x - 1}{x ^{3} + 6 x ^{2} + 2 x - 4} :

Maximum

(- 3.36903 \dots, - 0.22845 \dots),

Minimum

(0.17524 \dots, 0.23837 \dots),

Maximum

(1.69378 \dots, 0.03232 \dots)

f (x) = x + 1 + 3 - x

y = \frac{2}{5} x^{2}

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

f (x) = 9 ∣ x ∣

f (x) = - x cos (x) + sin (x)