Quote of the Day:
"I hear and I forget.
I see and I remember.
I do and I understand." -- Chinese Proverb.
Objectives:
The student will be able to graph step functions
(for example, the greatest integer function).
The student will be able to form the inverse function of
a given function.
The student will be able to graph piece-wise defined functions.
The student will be able to use functional notation and compute
the values of composite functions.
The student will be able to decompose functions.
1. Collect Homework Assignment.
2. Compostion of Functions
3. Decomposition of Functions
4. Types of Functions
(1) Piece-wise Defined Functions
(functions defined over different domains)
Examples:
(a) Cost of purchasing Graphing calculators
if n < 10, cost is $68.75 each
if 10 <= n <20 cost is $68.00 each
if 20 <= n <30 cost is $67.50 each
(b) Figuring Shipping on an internet order
for orders < $20.00, add $2.00
for orders between $20 and $100, add .10*cost of order
for orders > $100, add $12.00
(c) Definition of Absolute Value
(2) Step Functions
Examples:
(a) Greatest Integer Function
Graph of the Greatest Integer Function
(b) Click here for Postage Rates (Step function)
(c) Click here for Tax Table (Step function)
(d) Click here for Church Giving (Step function)
(3) Even / Odd Functions
f(x) is even if f(-x) = f(x) for all x.
f(x) is odd if f(-x) = -f(x) for all x.
Examples:
5. Other Functions (which will be discussed later)
I. Algebraic Functions
A. Explicit Functions
1. Polynomial Functions
a. Constant
b. Linear
c. Quadratic
d. Cubic
2. Rational Functions
B. Implicit Functions
e.g., xy = 3
II. Transcendental Functions
A. Trig Functions
B. Logarithmic Functions
C. Exponential Functions
6. Inverse Functions
Definition:
5. Miscellaneous Graphs
7. Assignment:
Read pages 6, 7, 27-30, 35, 51-54
p. 13 (9b, 10b, 31, 33, 35)
p. 36 Quick Check (1, 2, 4)
p. 36 (1a,b, 3c, 29, 31, 32a,d, 35, 41)
p. 63 (9, 10, 11)
Work on Mini Exam Review Sheet
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