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

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

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

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

Domain : x < - \frac{3}{4} or - \frac{3}{4} < x < 0 or x > 0

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

X Intercepts : (\frac{4.18623 E 15}{2.5 E 16}, 0), (- \frac{4.18623 E 15}{2.5 E 16}, 0), (\frac{2.95184 E 13}{1.25 E 13}, 0), (- \frac{2.95184 E 13}{1.25 E 13}, 0)

Asymptotes : Vertical x = - \frac{3}{4}, x = 0, Horizontal y = \frac{1}{4}

Extreme Points : Maximum (- 2.92869 \dots, 0.30918 \dots), Minimum (0.51379 \dots, - 3.12433 \dots)

Interval Notation

Domain : (- \infty, - \frac{3}{4}) \cup (- \frac{3}{4}, 0) \cup (0, \infty)

Range : (- \infty, \infty)

Solution steps

Domain of

\frac{x ^{- 2} + x ^{4} - 6}{3 x ^{3} + 4 x ^{4}} : x < - \frac{3}{4} or - \frac{3}{4} < x < 0 or x > 0

Range of

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

Axis interception points of

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

X Intercepts

: (\frac{4.18623 E 15}{2.5 E 16}, 0), (- \frac{4.18623 E 15}{2.5 E 16}, 0), (\frac{2.95184 E 13}{1.25 E 13}, 0), (- \frac{2.95184 E 13}{1.25 E 13}, 0)

Asymptotes of

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

Vertical

: x = - \frac{3}{4}, x = 0,

Horizontal

: y = \frac{1}{4}

Extreme Points of

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

Maximum

(- 2.92869 \dots, 0.30918 \dots),

Minimum

(0.51379 \dots, - 3.12433 \dots)

y = \frac{x ^{2}}{( ln ( x ) )}

f (x) = (x - 3)^{4} - 5

f (x) = \frac{x}{lo g _{2} ( x )}

f (x) = \frac{x}{x ^{2} - 5}

f (x) = \frac{x + 1}{x + 3}

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