1.9.2: Key Equations

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May 28, 2023
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- 1.9.1: Key Terms
- 1.9.3: Key Concepts

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Key Equations

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

Average rate of change

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

Composite function

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

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	$g (x) = a f (x)$ ( $a > 1$ )
Vertical compression	$g (x) = a f (x)$ $(0 < a < 1)$
Horizontal stretch	$g (x) = f (b x)$ $(0 < b < 1)$
Horizontal compression	$g (x) = f (b x)$ ( $b > 1$ )

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