Domain and Range

 

A. Linear Function
\(y = mx + c\)

 

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Domain

\(- \sim \: < x < \: \sim\)

 

Range

\(- \sim \: < y < \: \sim\)

B. Quadratic Function

Concave up

\(y = ax^2 + bx + c, \: a > 0\)

 

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Domain

\(- \sim \: < x < \: \sim\)

 

Range

\(\{y \geq y_{\text{min}}\}\)

 

Determine extreem value

\(x_p = - \dfrac {b}{2a}\)

Substitute \(x_{\text{p}}\) into the equation to find \(y_p\)

Concave down

\(y = ax^2 + bx + c, \: a < 0\)

 

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Domain

\(- \sim \: < x < \: \sim\)

 

Range

\(\{y \leq y_{\text{max}}\}\)

C. Root Function
\(y = \sqrt{x}\)

 

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Domain

\(x \geq 0\)

 

Range

\(y \geq 0\)

D. Rational Function
\(y = \dfrac 1x\)

 

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Horizontal Asymtote

\(y = 0\)

 

Vertical Asymtote

\(x = 0\)

 

Domain

\(\{x \neq 0\}\)

 

Range

\(\{y \neq 0\}\)

 

Exercise

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