General Information
-
The exam will be held on Thursday, September 27, from 5:30pm to 7:00pm, in Smith Labs 154.
-
Plan to arrive a few minutes early to allow time to distribute the exams.
-
The exam will cover material from sections 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 2.1, and 2.2 in the text.
-
Cell-phones should be turned OFF for the duration of the exam.
-
You may use a non-graphing, scientific calculator during the exam. No other calculator or electronic device may be used during the exam.
-
This is a closed-book exam. No books or notes may be used during the exam.
-
You will be expected to show all of your work. A correct answer with insufficient justification
may not receive full credit.
Topics
-
Functions and Graphs. (1.1) Know how to find the domain and range of a given function. Be able to graph basic functions (linear, quadratic, trig, exponential) and know how to obtain the formula for a function whose graph is obtained by shifting and/or stretching, and how to graph functions that are obtained by modifying the formula of a function whose graph is known. Know how to identify intervals on which a function is increasing or decreasing.
-
Linear and Quadratic Functions. (1.2) Know how to find the equation of a line that satisfies some given conditions. For a given quadratic function, you should be able to rewrite it by completing the square, find its roots, identify its maximum or minimum value, and sketch its graph.
-
Basic Classes of Functions. (1.3) Be familiar with the standard classes of functions: powers, polynomial, rational, exponential, logarithmic, trigonometric. Know how to determine the domain of any such function, as well as how to form compositions involving functions of these types and determine their domains.
-
Trigonometric Functions. (1.4) Be familiar with how the functions cosine and sine are defined in terms of the unit circle, as well as how the other trig functions are defined in terms of them. Given a right triangle, know how to represent the trig functions as ratios of its side lengths. Know the trig identities on page 28, and be able to use them as in the homework exercises.
-
Inverses. (1.5) Know the definition of the inverse of a function. Be able to determine whether or not a function is invertible. Know the relationship between the graphs of a function and its inverse. Know how to find the formula for the inverse of a given function, as well as its domain and range.
-
Exponentials and Logarithms. (1.6) Know how exponential functions and logarithms are related. Know the basic properties of exponentials and logs (pages 41 and 44).
-
Average and Instantaneous Rates of Change. (2.1) Know how to find the average rate of change of a function over an interval. Be able to estimate the instantaneous rate of change of a function at a point.
-
Evaluating Limits Graphically and Numerically. (2.2) Know how to find limits of a function using its graph. Also be able to evaluate limits of a function numerically by making tables of values.
Preparing for the Exam
The exam will consist of questions similar to those assigned on the worksheets (1 through 5), quizzes (1 through 3) and WebAssign (Assignments 1 through 3). Be sure you are familiar with how to solve these types of problems. Here are a some additional problems from the Chapter Review sections to use for practice. Solutions to the odd-numbered exercises are in the back of the text.
Chapter 1 Review, p. 53
Exercises 6-31, 40-42, 44, 46, 47, 51-55
Chapter 2 Review, p. 110
Exercises 1,2,5-10
