Chapter 1 Project

Analyzing Elementary Functions

In this project you will analyze various functions using many of the concepts developed in Chapter 1. Thoroughly analyze the following aspects of each function, explaining your methods and conclusions. Remember the "rule of four": use verbal, algebraic, graphic, and numeric approaches. For each function, create a table of values and a carefully drawn graph, and include them with your analysis.

(a) What are the domain and range of the function?

(b) What are its x- and y-intercepts?

(c) Identify any removable, jump, or infinite discontinuities.

(d) Report the intervals on which the function is increasing and the intervals on which it is decreasing.

(e) Is the function bounded above, below, both, or neither?

(f) Does it have any local or absolute maximum and minimum values? At which x values do these occur?

(g) Is the function even, odd, or neither? Is its graph symmetry? If so, describe the type of symmetry.

(h) Does the graph of the function have any horizontal and vertical asymptotes? If so, write the equations of the asymptotes.

(i) Is the function one-to-one? If so, determine the equation of the associated inverse function.

Function 1.

Function 2.

Function 3.

Function 4. int x = the greatest integer less than or equal to x.

Function 5.

Function 6.