For September 5

Section 1.1 Functions, Calculus Style

• To read: Through Example 6
• Be sure to understand: Examples 5 and 6

Email Subject Line: Math 101 9/5 Your Name

Reading Questions:

1. Give an example of a function that is defined by words, without an explicit formula.
2. Using the function m(x) in Example 4, what is m(2)?
3. Is the balloon in Example 5 rising or falling at time t=4 minutes? Explain.

For September 8

• To read: All
• Be sure to understand: Example 3; Example 4 part 3; Operations with constants

Email Subject Line: Math 101 9/8 Your Name

Reading Questions:

1. Explain why the graph of x^2+y^2=1 in Example 1 is not the graph of a function.
2. For which values of x is the graph in Example 3 increasing? decreasing?
3. How does the graph of f(x)+2 compare with the graph of f(x)? the graph of 2 f(x) to the graph of f(x)?

For September 10

• To read: All
• Be sure to understand: The Six views of the sine function; Example 1

• To read: All
• Be sure to understand: The Five Examples; the definition of domain and range of a function

Email Subject Line: Math 101 9/10 Your Name

Reading Questions:

1. Give the domain and range of the function f(x)=x^2.
2. Let g(t) = the world's human population t years C.E. Give the domain and range of g.
3. How can you recognize a periodic function from its graph?

For September 12

Section 1.5 A Field Guide to Elementary Functions

• To read: Pages 49-61
• Be sure to understand: The definition of an exponential function and the definition of a logarithm function.

Email Subject Line: Math 101 9/12 Your Name

Reading Questions:

1. What is the domain of the rational function r(x) = x^2/(x^2-1) in Example 3? Why?
2. Every exponential function f(x)=b^x passes through a common point. What is it? Why?
3. Every logarithmic function g(x)=log_b(x) passes through a common point. What is it? Why?

For September 15

• To read: Pages 61-65
• Be sure to understand: The sine and cosine function defined as circular functions (pg 62)

Email Subject Line: Math 101 9/15 Your Name

Reading Questions:

1. What are the domain and range of sin(x)?
2. What are the domain and range of tan(x)?
3. What is the period of the cosine function? How can you tell?

For September 17

• To read: Through Example 4
• Be sure to understand: The definition of the composition of two functions.

Email Subject Line: Math 101 9/17 Your Name

Reading Questions:

1. Let f(x)=x^2 and g(x)=sin(x) . What is (f o g)(x) ?
2. Let f(x)=x^2 and g(x)=sin(x) . What is (g o f)(x) ?
3. In Example 2, explain why (f o g)(-4) is undefined.

For September 19

For September 22

• To read: Through page 100
• Be sure to understand: Pages 94-96 on Rates, Amounts, and Cars: The Prime Example

Email Subject Line: Math 101 9/22 Your Name

Reading Questions: Look at the graphs of P(t) and V(t) on page 95.

1. Is the derivative of P positive or negative at t=5 ?
2. Is the second derivative of P positive or negative at t=5 ?
3. Give a value of t where the derivative of P is zero.

For September 24

• To read: All
• Be sure to understand: Examples 1, 4, and 5

Email Subject Line: Math 101 9/24 Your Name

Reading Questions:

1. What does the term "locally linear" mean?
2. Explain why the derivative of f(x)=|x| does not exist at x=0.

For September 26

Section 2.3 The Geometry of Derivatives

• To read: All
• Be sure to understand: The Extended Example beginning on page 118; The definitions of stationary point, local maximum and minimum, global maximum and minimum, concave up and concave down; The First Derivative Test

Email Subject Line: Math 101 9/26 Your Name

Reading Questions: Look at the graph of f ' in Example 2:

1. Where does f have stationary points?
2. Where is f increasing?
3. Where is f concave up?

For September 29

• To read: All
• Be sure to understand: The Second Derivative Test

Email Subject Line: Math 101 9/29 Your Name

Reading Questions:
Use the graphs of f, f ', and f ' ' on page 133.

1. By looking at the graph of f '', how can you tell where f is concave up and concave down?
2. By looking at the graph of f ', how can you tell where f is concave up and concave down?

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