1.1      Know the definition of a function. Be able to interpret the function if it is given algebraically, numerically or graphically. Review piecewise given functions and basic function properties such as symmetries and  increasing property.

1.2      Know the properties (formula, table, graph) of the following families of functions:
linear functions, polynomial functions, power functions, rational functions, exponential functions,
logarithmic functions, trigonometric functions.

1.3    Review function transformations and know their effect on the graph of a function. Be able to graph a function by showing each transformation steps must be used to obtain the graph from a basic simple function of the family. Understand the composition of functions. Be able to find a composite function if formulas, graphs or tables are given. Also be able to identify the simple functions and the steps of the composition to obtain  a given composite function.

1.4     Know how to use your graphing calculators to graph functions, how to set an appropriate viewing window, and how to zoom in. Be aware of the possible errors originating from rounding errors, graphing errors, overflows etc.  Know how to set up and  use the table function on your calculator.  Be familiar with the MAPLE commands we have been using in the lab.

1.5    Review exponential functions.  Correctly use the rules of exponents. Understand the application problems for exponential growth and decay and compound interest.

1.6      Be able to find the inverse of an invertible function algebraically, numerically and graphically. Be able to interpret the meaning of the original and the inverse function. Correctly use the rules of  logarithms. Review basic log expressions,their simplifications and log equations.

In general from chapter 1 understand the features of the graph of a function such as   x-intercept, y-intercept, domain,  range,  increasing/decreasing property,  asymptotes, symmetries, even/odd/neither property, periodic, one-to-one,  invertible property.

2.1    Be able to find the equation of the secant line between two given points and be able to predict the slope of the tangent line at one point. Know the relation between how to find slopes of secant lines, tangents lines and average and instantenouos velocity.

2.2    Know the definition of the limit of a function at a point  a.   Be able to find limits graphically and numerically.  Know what a vertical asymptote of a function is and how to find it.

2.3    Be familiar with the various limit laws. Be able to apply them to a specific limit calculation. Know the algebraic techniques that also help to find limits.  Know and be able apply the Squeeze theorem.

2.5    Know and understand the definition of continuity of a function for both a point  a  and for and interval [a,b].  Be able to decide if a function is continuous if the graph or the formula of the function is given.  Be familiar with the Theorems that follow from the limit laws from Section 2.3.   Know how to use continuity to evaluate limits. Know and be able apply the Intermediate Value Theorem.

2.6    Know the definition of the limit of a function at infinity.   Be able to find such limits algebraically, graphically and numerically.  Know what a horizontal asymptote of a function is and how to find it. Know how to graph polynomial and rational functions using the limit at infinity to specify their end behavior.

Recommended problems from the review sections:

pg 75        1-10
pg 76        1,2,45,8,9,10,14,19,20,22,24,25,26,27
pg 174      1-12
pg 175      1, 2, 4,6,11,14,19,32,33,39