Precalculus Review

Rational Functions

Reciprocal function. A function is called a reciprocal function if

$\displaystyle f(x) = \frac{ k }{x}$

with constant value $k \neq 0$ . The domain of

is $D = (-\infty,0)\cup (0,\infty)$ , that is, the set of all real values except

If , increases without bound as approaches 0 from the right, and decreases without bound as approaches 0 from the left. In short, we write

$\displaystyle f(x) \to \infty$ as $x \to 0+$ and $\displaystyle \quad f(x) \to -\infty$ as $x \to 0-$ . $\displaystyle$
If , decrease without bound as approaches 0 from the right, and increases without bound as approaches 0 from the left. In short, we write

$\displaystyle f(x) \to -\infty$ as $x \to 0+$ and $\displaystyle \quad f(x) \to \infty$ as $x \to 0-$ . $\displaystyle$

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