What is the range of (3x^3-30x+76)/(x^2-10x+25) ?

The range of (3x^3-30x+76)/(x^2-10x+25) is -infinity <f(x)<infinity

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range of (3x^3-30x+76)/(x^2-10x+25)

range

\frac{3 x ^{3} - 30 x + 76}{x ^{2} - 10 x + 25}

- \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{3 x ^{3} - 30 x + 76}{x ^{2} - 10 x + 25} : x < 5 or x > 5

Extreme Points of

\frac{3 x ^{3} - 30 x + 76}{x ^{2} - 10 x + 25} :

Maximum

(0.07507 \dots, 3.04058 \dots),

Minimum

(0.62075 \dots, 3.02928 \dots),

Minimum

(14.30416 \dots, 97.34790 \dots)

Find the range for the interval

- \infty < x < 5 : - \infty < f (x) < \infty

Find the range for the interval

5 < x < \infty : 97.34790 \dots \leq f (x) < \infty

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

- \infty < f (x) < \infty or f (x) \geq 97.34790 \dots

- \infty < f (x) < \infty

x + 2

cos (2 x)

f (x) = x^{6} (x - 1)^{5}

f (x) = \frac{100}{3} - \frac{x}{3}

\frac{0}{- 1}

What is the range of (3x^3-30x+76)/(x^2-10x+25) ?
The range of (3x^3-30x+76)/(x^2-10x+25) is -infinity <f(x)<infinity