# 1.9.2: Key Equations

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### Key Equations

 Constant function $f( x )=c, f( x )=c,$ where $c c$ is a constant Identity function $f( x )=x f( x )=x$ Absolute value function $f( x )=| x | f( x )=| x |$ Quadratic function $f( x )= x 2 f( x )= x 2$ Cubic function $f( x )= x 3 f( x )= x 3$ Reciprocal function $f( x )= 1 x f( x )= 1 x$ Reciprocal squared function $f( x )= 1 x 2 f( x )= 1 x 2$ Square root function $f( x )= x f( x )= x$ Cube root function $f( x )= x 3 f( x )= x 3$
 Average rate of change $Δy Δx = f( x 2 )−f( x 1 ) x 2 − x 1 Δy Δx = f( x 2 )−f( x 1 ) x 2 − x 1$
 Composite function $( f∘g )( x )=f( g( x ) ) ( f∘g )( x )=f( g( x ) )$
 Vertical shift $g(x)=f(x)+k g(x)=f(x)+k$ (up for $k>0 k>0$ ) Horizontal shift $g(x)=f(x−h) g(x)=f(x−h)$ (right for $h>0 h>0$ ) Vertical reflection $g(x)=−f(x) g(x)=−f(x)$ Horizontal reflection $g(x)=f(−x) g(x)=f(−x)$ Vertical stretch $g(x)=af(x) g(x)=af(x)$ ( $a>1 a>1$ ) Vertical compression $g(x)=af(x) g(x)=af(x)$ $(0 Horizontal stretch $g(x)=f(bx) g(x)=f(bx)$ $(0 Horizontal compression $g(x)=f(bx) g(x)=f(bx)$ ( $b>1 b>1$ )

1.9.2: Key Equations is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.