What is the range of f(x)=(x^2-16)/(-3x) ?

The range of f(x)=(x^2-16)/(-3x) is -infinity <f(x)<infinity

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range of f(x)=(x^2-16)/(-3x)

range

f (x) = \frac{x ^{2} - 16}{- 3 x}

- \infty < f (x) < \infty

Interval Notation

(- \infty, \infty)

Solution steps

Rewrite as

\frac{x ^{2} - 16}{- 3 x} = y

Simplify

\frac{x ^{2} - 16}{- 3 x} : - \frac{x ^{2} - 16}{3 x}

- \frac{x ^{2} - 16}{3 x} = y

Multiply both sides by

x

- \frac{x ^{2} - 16}{3} = y x

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

Discriminant

- \frac{x ^{2} - 16}{3} = y x : 9 y^{2} + 64

9 y^{2} + 64 \geq 0 :

True for all

y \in R

Therefore the range is

- \infty < f (x) < \infty

f (x) = \frac{1}{x + 25}

f (x) = \frac{x ^{2} + 5 x}{2 x ^{2} + 7 x - 15}

f (x) = \frac{6 x - 4}{2 x + 1}

y = - x^{2} - 2 x - 2

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

What is the range of f(x)=(x^2-16)/(-3x) ?
The range of f(x)=(x^2-16)/(-3x) is -infinity <f(x)<infinity