Determine Where a Function Is Increasing, Decreasing, or Constant

Constant Function

$f(x)=c$

Neither increasing nor decreasing

Identity Function

$f(x)=x$

Increasing

Quadratic Function

$f(x)=x^{2}$

Increasing on $(0, \infty)$

Decreasing on $(-\infty, 0)$

Minimum at $x=0$

Cubic Function

$f(x)=x^{3}$

Increasing

Reciprocal

$f(x)=\frac{1}{x}$ 

Decreasing $(-\infty, 0) \cup(0, \infty)$

Reciprocal Squared

$f(x)=\frac{1}{x^{2}}$ 

Increasing on $(-\infty, 0)$

Decreasing on $(0, \infty)$ 

Cube Root

$f(x)=\sqrt[3]{x}$

Square Root

$f(x)=\sqrt{x}$ 

Absolute Value

$f(x)=|x|$

Increasing on $(0, \infty)$

Decreasing on $(-\infty, 0)$