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MATH 105 Section 28
Instructor : Hyosang Kang
Lesson Plan
Review section 1.1Team guidelinesHomework problemSection 1.2Assignment
Function
A function is a rule which takes certain numbers as inputs and assigns to each input number exactly one output number.
Rule of FourWords, Tables, Graphs, and
FormulasA function can be described using
words, data in a table, points on a graph, or a formula.
Example 1 (Word)
Crickets chirp at a rate that increases as the temperature.
The temperature is the number of times a cricket chirps in 15 seconds (1/4 minute) plus 40.
Example 1 (Table)
R, chirp rate (chirps/minute) T, predicted temperature
20 45
40 50
60 55
80 60
100 65
120 70
140 75
160 80
Example 1 (Graph)
Chirp rate and temperature
0
50
100
150
200
20 40 60 80 100 120 140 160
chirp rate (chirps/min)
tem
pera
ture
Example 1 (Formula)
T=1/4R+40T: temperature, R: chirp rate
Function notation
To indicate that a quantity Q is a function of a quantity t, we abbreviate Q is a function of t to
Q equals “f of t”
and, using function notation, to
Q=f(t)
Vertical Line Test
If there is a vertical line which intersects a graph in more than one point, then the graph does not represent a function.
Team Guidelines
How to make a group?Decide the roles ( Scribe, Clarifier,
Reporter, Manager )First meeting time and place
Rate of Change (1)
The average rate of change, or rate of change, of Q with respect to t over an interval is
‘Changes in Q’rate of change = -----------
‘Changes in t’
Rate of Change (2)
If Q=f(t), then it is equal to say
f(b) - f(a) ---------- b – a
a: initial value of t, b: final value of t
Worksheet 1.2
Omit ‘per minute’ in problem 2Find the rate of changes of functions, re
presented by the table E, F, and G, on each intervals
Use y = f(x)
Worksheet 1.2
E
050
100150200250300350400450
0 5 10 15 20 25
Worksheet 1.2
F
050
100150200250300350400450
0 5 10 15 20 25
Worksheet 1.2
G
050
100150200250300350400450
0 5 10 15 20 25
Increasing / Decreasing Function
If Q=f(t) for t in the interval a≤t≤b, f is an increasing function if the value of
f increases as t increases in this interval.
f is a decreasing function if the value of f decreases as t increases in this interval.
Caution!TRUE: If a function is increasing
(decreasing) on an interval, then the average rate of change is positive (negative) on the interval.
NOT TRUE: if the average rate of change of a function is positive (negative) on an interval, then the function is increasing (decreasing) on the interval.
Example 4 (page 14)
Problem 9 (page 15)
Do problem 10 if you finished early
Problem 9 (page 15)
Key words of today
The Rule of FourAverage rate of change of a function ove
r an interval and its expressionThe average rate of change and the slo
pe of the secant line joining the point (a,f(a)) and (b,f(b)).
Increasing and decreasing functions
Assignment
Buy & Bring: TI-83 or equivalentRead: section 1.3 and handoutsDo: Section 1.1-8,13,15,18
Section 1.2-3,4,6,8,10,15Team Homework (due 9/16/05):
1.1-18, 1.2-16, 1.3-22, 1.6-6