第3章関数Functions

Key Equations重要な式

Constant function定数関数	$f (x) = c,$ where $c$ is a constant $f (x) = c$ ここで $c$ は定数
Identity function恒等関数	$f (x) = x$
Absolute value function絶対値関数	$f (x) = \| x \|$
Quadratic function二次関数	$f (x) = x^{2}$
Cubic function三次関数	$f (x) = x^{3}$
Reciprocal function逆数の関数	$f (x) = \frac{1}{x}$
Reciprocal squared function逆数の二乗の関数	$f (x) = \frac{1}{x^{2}}$
Square root function平方根の関数	$f (x) = \sqrt{x}$
Cube root function三乗根の関数	$f (x) = \sqrt[3]{x}$

Average rate of change平均変化率

\frac{Δ y}{Δ x} = \frac{f (x_{2}) - f (x_{1})}{x_{2} - x_{1}}

Composite function合成関数

(f \circ g) (x) = f (g (x))

Vertical shift縦の平行移動	$g (x) = f (x) + k$ (up for $k > 0$ ) $g (x) = f (x) + k$ ( $k > 0$ なら上へ)
Horizontal shift横の平行移動	$g (x) = f (x - h)$ (right for $h > 0$ ) $g (x) = f (x - h)$ ( $h > 0$ なら右へ)
Vertical reflection縦の対称移動	$g (x) = - f (x)$
Horizontal reflection横の対称移動	$g (x) = f (- x)$
Vertical stretch縦の拡大	$g (x) = a f (x)$ ( $a > 0$ )
Vertical compression縦の縮小	$g (x) = a f (x)$ $(0 < a < 1)$
Horizontal stretch横の拡大	$g (x) = f (b x)$ $(0 < b < 1)$
Horizontal compression.横の縮小	$g (x) = f (b x)$ ( $b > 1$ )