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

The range of f(x)=(x^2-2x+1)/(x^3-3x^2) is -infinity <f(x)<infinity

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range of f(x)=(x^2-2x+1)/(x^3-3x^2)

range

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

- \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 ^{2} - 2 x + 1}{x ^{3} - 3 x ^{2}} : x < 0 or 0 < x < 3 or x > 3

Extreme Points of

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

Maximum

(1, 0)

Find the range for the interval

- \infty < x < 0 : - \infty < f (x) < 0

Find the range for the interval

0 < x < 3 : - \infty < f (x) \leq 0

Find the range for the interval

3 < x < \infty : 0 < f (x) < \infty

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

f (x) < 0 or f (x) \leq 0 or f (x) > 0

- \infty < f (x) < \infty

(6.8) (5.1)

f (x) = \frac{4}{5} x - 5

- \frac{5}{2 x ^{\frac{3}{2}}}

f (x) = x^{2} + 3 x + 5

x - 3 y = 15

What is the range of f(x)=(x^2-2x+1)/(x^3-3x^2) ?
The range of f(x)=(x^2-2x+1)/(x^3-3x^2) is -infinity <f(x)<infinity