Linear and Exponential Functions

Th  ¬  HH1.1, (1.2)

 

agree on homework days / realign triads /

 

Definition of function (and other reading checks): symbolic/graphical/numerical

 

Linear Functions

How do you know one if you see one? AND How do you write down a generic one?

Great Linear Functions I Have Known:

§ WPPSS electric power demand projection / the ocean horizon / the photoelectric effect / depreciation / gravitational potential energy /

§ conversions: exchange rates / temperature scales / building height above datum /

Linear Functions Around Us:

§ height as function of number of steps on a staircase / electric bill and time (via wattage)

 

• family of linear functions: the idea of parameter

 § special values of the parameters: b = 0 / m = 0 / m = ¥ /

• difference quotient

• proportionality

 

what is a full solution? use 1.1.30 as worked example

§ use of the blue boxes

§ technique: identification of unknowns; elimination of unknowns

§ explanation: what is each step, in words, and why it is justified?

§ interpretation

 

Exponential Functions: recognition / generic form / properties

the other rule of exponents:  eax=(ea)x

 

calculator work:

§ check: graph an exponential, find its value using TRACE at a given x

§ lists and families of functions

§ which wins, exponential or linear function?