Chapter 2

Review

This review is basically a check-off list of the important concepts and processes from chapter 2 along with some reminders of the most common misconceptions.

Section 2.1 ~ Functions

• Know the definition of Function and be able to explain what it means to be and not be a function. (Look at the Chapter 2 Overview.)
• Determine if a given correspondence, in various forms (graphic, tabular, diagrammatic), is or is not a function.
• Know what is meant by Independent and Dependent Variable and their relationship to Inputs and Outputs.
• Explain the Domain and Range of a function in terms of Inputs and Outputs and be able to determine the domain and range of a given function in various forms (graphic, tabular, algebraic).
• Be able to apply the Vertical Line Test and to Explain why it works.

Section 2.2 ~ Graphs of Functions

• Know the relationship between Zeros, Roots, and Solutions of a function and how to find them for various forms of a function.
• Know the graphs of a few Simple Prototype functions.
• Be able to work with Translations & Reflections of functions both graphically and algebraically.
• Understand the different types of Symmetry, which represents an Even and which an Odd function.
• Be able to determine if a given function is Even, Odd, or Neither, both Graphically and Algebraically, and to give an Example of a function of each type.
• Find intervals of Increasing and Decreasing behavior of a function, it's Turning points, and it's Local Maximums and Local Minimums.

Section 2.3 ~ Combinations of Functions

• Be able to determine the Sum, Difference, Product, and Quotient of given functions and their Domains.
• Be able to compute and evaluate Compositions of functions and determine their domains, given functions in Graphic, Algebraic or Tabular form.

• The domain of the composition of two functions is often NOT the domain of the resulting algebraic form of the composition.

Section 2.4 ~ Inverses of Functions

• Know the definition of Inverse function and be able to use the definition to determine if two given functions are inverses of each other.
• Understand the relationships between the Domains and Ranges of a function and its inverse.
• Know the definition of a one-to-one function and why it is important.
• Be able to apply the Horizontal Line Test and explain what it means and why it works.
• Be able to find the Inverse of a 1-1 function algebraically.
• Be able to find the Inverse of a function given in a table.
• Be able to sketch the graph of the inverse function given the graph of a 1-1 function and explain why this process works.

Section 2.5 ~ Selected Functions

• Be able to Identify Linear, Quadratic and Piece-Wise Defined functions.
• Know the Standard form of a quadratic function and its relationship to its graph, which is a Parabola.
• Be able to determine the Vertex of a parabola by “completing the square”.
• Determine the algebraic form of a quadratic function with given attributes.
• Understand and be able to evaluate Piece-Wise Defined functions.
• Know the following Piece-Wise defined functions: Absolute Value, Step, Floor, and Ceiling Functions.

Hints

There is a Self-Study Check Up For Chapter 2 in the printed Study Guide. It gives a list of problems from the Chapter 2 Review and Test in the Textbook that would be a good review of the chapter 2 material.