Domain and range

A. Linear Function
$y = m x + c$	Domain $- \sim < x < \sim$ Range $- \sim < y < \sim$
B. Quadratic Function
Concave up $y = a x^{2} + b x + c, a > 0$	Domain $- \sim < x < \sim$ Range ${y \geq y_{min}}$ Determine extreem value $x_{p} = - \frac{b}{2 a}$ Substitute $x_{p}$ into the equation to find $y_{p}$
Concave down $y = a x^{2} + b x + c, a < 0$	Domain $- \sim < x < \sim$ Range ${y \leq y_{max}}$
C. Root Function
$y = \sqrt{x}$	Domain $x \geq 0$ Range $y \geq 0$
D. Rational Function
$y = \frac{1}{x}$	Horizontal Asymtote $y = 0$ Vertical Asymtote $x = 0$ Domain ${x \neq 0}$ Range ${y \neq 0}$

A. Linear Function

y = m x + c

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Domain

$- \sim < x < \sim$

Range

$- \sim < y < \sim$

B. Quadratic Function

Concave up

$y = a x^{2} + b x + c, a > 0$

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Domain

$- \sim < x < \sim$

Range

${y \geq y_{min}}$

Determine extreem value

$x_{p} = - \frac{b}{2 a}$

Substitute $x_{p}$ into the equation to find $y_{p}$

Concave down

$y = a x^{2} + b x + c, a < 0$

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Domain

$- \sim < x < \sim$

Range

${y \leq y_{max}}$

C. Root Function

y = \sqrt{x}

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Domain

$x \geq 0$

Range

$y \geq 0$

D. Rational Function

y = \frac{1}{x}

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Horizontal Asymtote

$y = 0$

Vertical Asymtote

$x = 0$

Domain

${x \neq 0}$

Range

${y \neq 0}$