What is the range of f(x)=(x^3+4x^2-2)/(x^2-9) ?

The range of f(x)=(x^3+4x^2-2)/(x^2-9) is -infinity <f(x)<infinity

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range of f(x)=(x^3+4x^2-2)/(x^2-9)

range

f (x) = \frac{x ^{3} + 4 x ^{2} - 2}{x ^{2} - 9}

- \infty < f (x) < \infty

Interval Notation

(- \infty, \infty)

Solution steps

Find the minimum and maximum value in each defined interval and unite the results

Domain of

\frac{x ^{3} + 4 x ^{2} - 2}{x ^{2} - 9} : x < - 3 or - 3 < x < 3 or x > 3

Extreme Points of

\frac{x ^{3} + 4 x ^{2} - 2}{x ^{2} - 9} :

Maximum

(0, \frac{2}{9}),

Minimum

(6.16661 \dots, 13.24992 \dots)

Find the range for the interval

- \infty < x < - 3 : - \infty < f (x) < \infty

Find the range for the interval

- 3 < x < 3 : - \infty < f (x) \leq \frac{2}{9}

Find the range for the interval

3 < x < \infty : 13.24992 \dots \leq f (x) < \infty

Combine the ranges of all domain intervals to obtain the function range

- \infty < f (x) < \infty or f (x) \leq \frac{2}{9} or f (x) \geq 13.24992 \dots

- \infty < f (x) < \infty

x^{3} - 5

f (x) = 6 x^{4} + 32 x^{3}

f (x) = 5 x^{5}

\frac{x - 1}{x}

(- 4 - 7) (- 4 - 6)

What is the range of f(x)=(x^3+4x^2-2)/(x^2-9) ?
The range of f(x)=(x^3+4x^2-2)/(x^2-9) is -infinity <f(x)<infinity