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

2. FAMILY OF FUNCTIONS

3. FAMILY OF FUNCTIONS QUADRATIC CONSTANT LINEAR EXPONENTIAL RATIONAL
PERIODIC
PIECEWISE
STEP

4. 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

5. CONSTANT

6. 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

7. LINEAR

8. 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

9. QUADRATIC

10. 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

11. RATIONAL

12. 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 · 𝑥

13. EXPONENTIAL

14. 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”

15. PERIODIC

16. 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

17. STEP

18. 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 if 3 ˂ x ˂ 10, and y = 500 if x ≥ 10

19. PIECEWISE