Parent EquationGeneral FormsTransforming

Parent Equation

O The simplest form of any functionO Each parent function has a

distinctive graphO We will summarize these in the next

few slides

ConstantO f(x)=a; where a is any number

LinearO f(x)=x

Absolute Value

Exponential Value

LogarithmicO y=lnx

Square Root/Radical

Cube Root

QuadraticO f(x)=x2

CubicO f(x)=x3

ReciprocalO Same as a Rational Graph

Rational

SineO y=sinx

CosineO y=cosx

TangentO y=tanx

Constant FunctionO f(x)=a; where a is any numberO Domain: all real numbers O Range: a

Linear FunctionO f(x)=xO Domain: all real numbersO Range: all real numbers

TransformationsLinear and Quadratic

Vertical TranslationsO Positive Shift (Shift up)

O Form: y=f(x)+b where b is the shift up

O Negative Shift (Shift down)O Form: y=f(x)-b where b is the shift

down

Horizontal TranslationsO Shift to the right

O Form: y=f(x-h) O The negative makes you think left,

but actually means right hereO Shift to the left

O Form y=f(x+h)O This would shift to the left of the

origin

Vertical Stretch and Compression

O If y=f(x), then y=af(x) gives a vertical stretch or compression of the graph of f

O If a>1, the graph is stretched vertically by a factor of a

O If a<1, the graph is compressed vertically by a factor of a

Horizontal Stretch and Compression

O If y=f(x),then y=f(bx) gives a horizontal stretch or compression of the graph of f

O If b>1, the graph is compressed horizontally by a factor of 1/b

O If b<1, the graph is stretched horizontally by a factor of 1/b

ReflectionO If y=f(x), then y=-f(x) gives a

reflection of the graph f across the x axis

O If y=f(x), then y= f(-x) gives a reflection of the graph f across the y axisl