FAMILIES OF FUNCTIONS

Functions are often grouped into families according to the form of their defining formulas, or other commom characteristics.

The Constant function

The graph of the constant function f(x) =k is the graph of the equation y = k, which is the horizontal line. If we vary k then we obtain a family of horizontal lines.

The Linear function 

Characteristics   Domain : All real numbers Range : All real numbers   Intercepts: x-intercept = (0, 0)   y-intercept = (0, 0) Slope : End behavior :

Transformations of the linear function

The Quadratic function (The Parabola)

Characteristics   Domain : All real numbers Range: All positive numbers Zeroes :  0 Axis of symmetry:   x = 0 Coordinate of vertex :   (0,0) Minimum or Maximum :     minimum = (0, 0) Interval of Increase/ Decrease :       Rate of Change :     End behavior :

Transformations of the quadratic function

The Cubic Function

Characteristics   Domain : All real numbers  Range : All real numbers  Zeroes : (0,0)  Rate of Change :   Interval of Increase/ Decrease:         End Behavior:

Transformations of the Cubic function 

The Absolute value function

Characteristics Domain:    Range    Zeroes:    Rate of Change    Interval of Increase/Decrease  Increasing on   Decreasing on End Behavior

Transformation of The Absolute Value Function

The Square root (or Radical) function

Characteristics   Domain :    Range :    Zeroes :    Rate of Change :    Interval of Increase/Decrease    End Behavior

Transformations of the Square root function

The Rational function

Characteristics   Domain :   Range :   Rate of change:    Interval of Increase/Decrease : Decreasing on   End Behavior:

Transformations of the rational function

Problem Set