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

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

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

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

Domain : x < - 1 or - 1 < x < 0 or x > 0

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

X Intercepts : (1, 0)

Asymptotes : Vertical x = - 1, x = 0, Slant y = x - 2

Extreme Points : Maximum (- 3.79804 \dots, - 8.31879 \dots), Minimum (- 0.39190 \dots, 24.25944 \dots)

Solution steps

Domain of

\frac{( x - 1 ) ( x ^{2} + 4 )}{x ( x + 1 )} : x < - 1 or - 1 < x < 0 or x > 0

Range of

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

Axis interception points of

\frac{( x - 1 ) ( x ^{2} + 4 )}{x ( x + 1 )} :

X Intercepts

: (1, 0)

Asymptotes of

\frac{( x - 1 ) ( x ^{2} + 4 )}{x ( x + 1 )} :

Vertical

: x = - 1, x = 0,

Slant

: y = x - 2

Extreme Points of

\frac{( x - 1 ) ( x ^{2} + 4 )}{x ( x + 1 )} :

Maximum

(- 3.79804 \dots, - 8.31879 \dots),

Minimum

(- 0.39190 \dots, 24.25944 \dots)

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