MATH 2431 – Summer 2012

Project 2 – Algebra – Due: 21 June 2012

You must complete the project in a group of two students. Normally, all members of the group will receive the same grade; however, the instructor reserves the right to conduct individual interviews over the content of the project and to assign different grades to different members of the group.

Graphing functions is extremely important for successfully completing calculus I. More importantly,
knowing the shapes of the graphs of functions will be helpful in calculus I.
In this project, you will learn the `Plot`

function of mathematica and its arguments and you
will make some conclusions from your work on this project.
You will be graded on the quality and clarity of your written
presentation as well as the mathematical accuracy of your paper.

To label your work, use comments. For example, use the following to start your project (after every line, use SHIFT-ENTER to execute):

(* Your Name *)

(* Partner's Name *)

(* Math2431-100 *)

(* Summer 2012 *)

(* Project 2 *)

There are two required arguments for the `Plot`

function: 1. the expression of the function and 2. the interval on which you want the graph.
Example: Graph f(x) = x^{2} – 5x – 2 on [–10, 10]

`Plot[x^2-5x-2,{x,-10,10}]`

Alternatively, you can store x^{2} – 5x – 2
into f(x):

`f[x_] := x^2-5x-2`

Plot[f[x],{x,-10,10}]

To zoom in or out, simply change the interval as needed:

`Plot[f[x],{x,-1,6}]`

Alternatively, use the additional `PlotRange`

argument:

`Plot[f[x],{x,-10,10},PlotRange->{-10,10}]`

Graph the following functions using mathematica and describe their shape, asymptotes (if any), domain (in interval notation), and range (in interval notation). 0.4 points each. Zoom in/out where necessary:

- f(x) = 3x – 2
- f(x) = 2x
^{2}– 5 - f(x) = – x
^{2}+ 5x + 1 - f(x) = – x
^{3}+ 2x + 3 - f(x) = x
^{3}+ 3x^{2}+ 5x - f(x) = 3
^{x} - f(x) = 2
^{– x} - f(x) = 0.6
^{x} - f(x) = √(x + 3); (use
`Sqrt[x+3])`

- f(x) = log
_{3}(x + 5); (use`Log[3,x+5])`

- f(x) = log
_{0.5}(2 – x); (use`Log[0.5,2-x])`

- f(x) = | 3 – 2x |; (use
`Abs[3-2x])`

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```Please follow these guidelines when preparing your report:

- Find a partner with whom you will complete the project. One person in the project needs to send the
instructor an email in iCollege and cc: your partner. Type your partner's name
and the project number on the Subject line of the email. This email is due on or before 10:00 a.m. on 18 June (1 point deducted if not completed).
- Each function must be graphed in order and clearly labeled.
- The Mathematica code is to be submitted by email in iCollege on or before 10:00 a.m. on the due date.
- The summary of the shape, asymptote(s) (if any), domain (in interval notation), and range
(in interval notation) must be typed (you may handwrite any unusual mathematical symbols, e.g., ∞) and submitted in class on or before 10:00 a.m. on the due date.
- Use mathematically correct notation.
- Do not use any cover page or report cover.
- Turn in one paper per group. The instructor will keep all papers. Make a copy for your files before turning in your paper.
- Clearly explain your reasoning. Use complete, grammatically-correct sentences or complete mathematical sentences.