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 QUADRATIC CONSTANT LINEAR EXPONENTIAL RATIONAL PERIODIC PIECEWISE STEP

constant RULE: y = b y = total 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 C:\Users\cobrien\Documents\FINDING THE EQUATION OF A LINE.pptx RULE: y = ax + b slope form ax + by + c = 0 standard form ax + by = c general form x, y = points on the line a = slope of the line (Rise over run ∆𝑦 ∆𝑥 = 𝑦 1 − 𝑦 2 𝑥 1 − 𝑥 2 ) b = initial value (y – intercept: when x = 0) FUNCTION SITUATION: A woman climbs a hill starting at 10m above sea level and ascends at 5m/min y = 5x + 10

LINEAR

quadratic RULE: y = a · 𝑥 2 y = total x = independent variable a = parameter (Minimum / Maximum values) FUNCTION SITUATION: A building is constructed as quickly and as tall above ground as it’s foundation below ground. Y = total time (days) constructing both x = meters high/low y = 2.5 𝑥 2

QUADRATIC

rational RULE: y = 𝑎 𝑥 x · y = a y = total x = independent variable a = parameter Inversely proportionate (as x increases – y decreases and vise versa) FUNCTION SITUATION: It takes 400 man hours to build a deck. Every man working shares the workload evenly. y = 400 𝑥 x = total number of men working y = the total hours each man works

RATIONAL

exponential RULE: y = a 𝑐 𝑥 y = total a = initial value c = base x = time limit c ˃ 1 graph increases 0 ˂ c ˂ 1 graph decreases FUNCTION SITUATION: Zombie Apocalypse – 2 zombies multiply 3 times a day. Y = total zombies. A = initial value. C = how much it multiplies. X = number of days y = 2 · 3 𝑥 Credit card interest – 12%/year on a $2000 purchase. Y = total amount owed. A. initial value owed. C = interest rate. X = time y = 2000 · 1.12 𝑥

EXPONENTIAL

periodic RULE: y = the rule where x is located (varies) AFTER FINDING WHERE IN THE LINE X GOES. GO BACK TO INITIAL PERIOD (CYCLE) TO FIND WHERE THE Y GOES FREQUENCY = 1 𝑃 FUNCTION SITUATION: “THE SNOWMAN”

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 = 20x + 50 if x ≤ 3, y = 12x + 250 if 3 ˂ x ˂ 10, and y = 500 if x ≥ 10

PIECEWISE