MATH 255A, Review for Midterm Test 1

Test topics

1. Functions, domains, ranges, composite functions (1.3)
2. Linear, quadratic, polynomial, rational functions. Graphs. Transformations of graphs (1.1,1.4,1.5)
3. Exponential and logarithmic functions. Solving exponential and logarithmic equations. Graphs. (2.1,2.2)
4. Exponential growth and decay (word problems) (2.3)
5. Trigonometric functions. Graphs. (2.4)
6. Continuity of functions. Basic types of discontinuities: jumps, asymptotes, gaps. Piecewise defined functions (3.2)
7. Limits of functions. Left and right limits, two-sided limits. Limits at infinity (3.1)
8. Average rate of change of a function on an interval (3.3)

Formulas/facts you need to know for the test

• Definitions: domain, range, intercepts, asymptotes
• Graphs of elementary functions (linear, quadratic, rational, power, exponential, logarithmic, trigonometric)
• Properties of the exponential/logarithmic functions
• Radian measure. Values of trigonometric functions for typical angles (0, pi/6, pi/4, pi/3, pi/2, etc.)
• Formula for the exponential growth/decay
• Different forms of equations for straight lines

Preparation for the test

Problems on the test will not be taken from the homework/practice problems but they will be generally similar. The best way to prepare is to study examples in the lectures and in the book and to solve practice problems (think about how to solve it, rather than look in the answer). Old exams are available at http://www.csun.edu/~panferov/math255a_f07/ and http://www.csun.edu/~panferov/math255a_s08/

Format of the test

Problems on the test will not be taken from the homework but they will generally be similar. You will need to provide a complete solution for each problem, showing all steps. You may get partial credit for solutions that are not completely correct as long as you have the right ideas and explain them. The test will be closed books/notes. A simple scientific calculator (example: TI-30XII) is allowed, but it is not required to answer the questions. Graphing calculators (example: TI-83, 84, 89) may not be used.