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Key Equations

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