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Mathematics LibreTexts

1.9.2: Key Equations

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    116006
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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 ( fg )( x )=f( g( x ) ) ( fg )( 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(xh) g(x)=f(xh) (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 )

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