Key Equations

Key Equations

Constant function	$f\left(x\right)=c,$ where $c$ is a constant
Identity function	$f\left(x\right)=x$
Absolute value function	$f\left(x\right)=\left|x\right|$
Quadratic function	$f\left(x\right)=x^2$
Cubic function	$f\left(x\right)=x^3$
Reciprocal function	$f\left(x\right)=\frac{1}{x}$
Reciprocal squared function	$f\left(x\right)=\frac{1}{x^2}$
Square root function	$f\left(x\right)=\sqrt{x}$
Cube root function	$f\left(x\right)=\sqrt[3]{x}$

Average rate of change

$\frac{\Delta y}{\Delta x}=\frac{f\left(x_2\right)-f\left(x_1\right)}{x_2-x_1}$

Composite function

$\left(f\circ g\right)\left(x\right)=f\left(g\left(x\right)\right)$

Vertical shift	$g(x)=f(x)+k$ (up for $k>0$ )
Horizontal shift	$g(x)=f(x-h)$ (right for $h>0$ )
Vertical reflection	$g(x)=-f(x)$
Horizontal reflection	$g(x)=f(-x)$
Vertical stretch	$g(x)=af(x)$ ( $a>0$ )
Vertical compression	$g(x)=af(x)$ $(0<a<1)$
Horizontal stretch	$g(x)=f(bx)$ $(0<b<1)$
Horizontal compression.	$g(x)=f(bx)$ ( $b>1$ )