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?