FAMILY OF FUNCTIONS CONSTANT zero degree polynomial LINEAR

FAMILY OF FUNCTIONS CONSTANT – zero degree polynomial LINEAR – first degree polynomial QUADRATIC – second degree polynomial RATIONAL – inverse relation EXPONENTIAL PERIODIC STEP PIECEWISE

FAMILY OF FUNCTIONS

FAMILY OF FUNCTIONS CONSTANT LINEAR EXPONENTIAL RATIONAL PERIODIC QUADRATIC STEP PIECEWISE

CONSTANT � RULE: y = total y = b b = initial value (y-intercept) FUNCTION SITUATION: � A person pays $68 per month for an unlimited bus pass y = 68 � The cost of a hall rental is $700 no matter how many people / no matter how long y = 700

CONSTANT

LINEAR �

LINEAR

QUADRATIC �

QUADRATIC

RATIONAL �

RATIONAL

EXPONENTIAL �

EXPONENTIAL

PERIODIC �

PERIODIC

STEP � RULE: CHOOSE FROM THE FAMILY OF FUNCTIONS – y = b, y = ax + b � ≥ ≤ • = included in the line � ˂ ˃ ◦ = not included in the line FUNCTION SITUATION: � A gymnasium charges $40 /hour to use for the first 3 hours and charges an additional $20 for every hour after that

STEP

PIECEWISE � RULE: choose the appropriate family of function rule (rule changes as the scenario for x changes) � y = a total based upon choosing the right scenario for x FUNCTION SITUATION: � A woman gets paid on commission. She earns y = 20 x + 50 if x ≤ 3, y = 12 x + 250 if 3 ˂ x ˂ 10, and y = 500 if x ≥ 10

PIECEWISE