What is the range of (x^2)/(x+2) ?

The range of (x^2)/(x+2) is f(x) = 0

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range of (x^2)/(x+2)

range

\frac{x ^{2}}{x + 2}

f (x) \leq - 8 or f (x) \geq 0

Interval Notation

(- \infty, - 8] \cup [0, \infty)

Solution steps

Rewrite as

\frac{x ^{2}}{x + 2} = y

Multiply both sides by

x + 2

x^{2} = y (x + 2)

The range is the set of y for which the discriminant is greater or equal to zero

Discriminant

x^{2} = y (x + 2) : y^{2} + 8 y

y^{2} + 8 y \geq 0 : y \leq - 8 or y \geq 0

Check if the range interval endpoints are included

y = - 8 :

Included

y = 0 :

Included

Therefore the range is

f (x) \leq - 8 or f (x) \geq 0

x - 3 + 2

0.577

f (x) = 13 x + \frac{1}{x}

5.5556 x^{2}

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

What is the range of (x^2)/(x+2) ?
The range of (x^2)/(x+2) is f(x)<=-8\lor f(x)>= 0