Mathematics 133 – Intensive Calculus for Science 1 Things to Know – Quiz 2 September 13, 2000

The second graded quiz of the semester will be given in class on Friday, September 15. There will be three or four questions similar to problems from the second problem set. You should know the following material.

1) Inverse functions. Know:

a) How to tell whether or not a function is invertible from its graph,

b) How to derive a formula for the inverse function f^{−1} from a formula for f,

c) How to sketch the graph of the inverse function from the graph of f.

2) The logarithm functions f(x) = log_{a}(x) and their properties a) g(x) = log_{a}(x) is the inverse function of the exponential function f(x) = a^{x}.

b) Formulas for logs of products, quotients, powers and how to apply them

c) The shapes of the graphs y = log_{a}(x)

d) Using logarithms to solve equations involving exponentials

e) The natural logarithm function f(x) = ln(x) (the logarithm function with base a = e = 2.71828 ⋯)

Good Review Problems:

1) Section 1.5/problems like 8-11, 17, 18

2) Section 1.6/problems like 2-8, 13-17, 27

3) Section 1.7/problems like 2-7, 24-27, 31