Power Functions (VCE SSCE Mathematical Methods): Flashcards

$f(x) = x^r$ where $r$ is rational

If $x_2 > x_1$ then $f(x_2) > f(x_1)$

$f(-x) = -f(x)$ (rotational symmetry about origin)

$f(-x) = f(x)$ (reflective symmetry about y-axis)

$\mathbb{R} \setminus \{0\}$ (all reals except zero)

$\mathbb{R}^+$ (positive real numbers only)

The $n$th root of $a$

$\mathbb{R}^+ \cup \{0\}$ (non-negative numbers)

$\mathbb{R}$ (all real numbers)

Horizontal: $y=0$, Vertical: $x=0$ (both axes)