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MATH 105 Section 28 Instructor : Hyosang Kang. Lesson Plan Review section 1.1 Team guidelines...
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Transcript of MATH 105 Section 28 Instructor : Hyosang Kang. Lesson Plan Review section 1.1 Team guidelines...
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MATH 105 Section 28
Instructor : Hyosang Kang
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Lesson Plan
Review section 1.1Team guidelinesHomework problemSection 1.2Assignment
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Function
A function is a rule which takes certain numbers as inputs and assigns to each input number exactly one output number.
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Rule of FourWords, Tables, Graphs, and
FormulasA function can be described using
words, data in a table, points on a graph, or a formula.
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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.
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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
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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
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Example 1 (Formula)
T=1/4R+40T: temperature, R: chirp rate
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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)
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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.
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Team Guidelines
How to make a group?Decide the roles ( Scribe, Clarifier,
Reporter, Manager )First meeting time and place
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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’
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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
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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)
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Worksheet 1.2
E
050
100150200250300350400450
0 5 10 15 20 25
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Worksheet 1.2
F
050
100150200250300350400450
0 5 10 15 20 25
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Worksheet 1.2
G
050
100150200250300350400450
0 5 10 15 20 25
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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.
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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.
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Example 4 (page 14)
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Problem 9 (page 15)
Do problem 10 if you finished early
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Problem 9 (page 15)
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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
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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