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