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Parent Equation. General Forms Transforming. Parent Equation. The simplest form of any function Each parent function has a distinctive graph We will summarize these in the next few slides. Constant. f(x)=a; where a is any number. Linear. f(x)=x. Absolute Value. Exponential Value. - PowerPoint PPT Presentation
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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