Mat-221/ Graded Work 4/ Fall 2010/ Halsey (50 Points)
Due at the beginning of class on Wednesday, September 22nd
You are to complete all work and explanations for this assignment using MathCad.
Your work should be well laid out and easy to follow.
You must submit a hard copy of your work, making sure you staple multiple sheets.
Please remember to save often!!!
Remember, your layout of the work and your written explanations must be your own. You may
certainly seek help with general mathematical ideas, as well as general ideas about using MathCad.
You may also discuss the material together, but should not be doing your final write up together, or
with the help of anyone in the math lab. I need to be grading YOUR work.
1.
You will be working with the function f (x)
9x 2 27x 18
4x 2 4x 8
a. (12 points) Use MathCad to determine the x intercept(s), y intercept, and values(s) where the
function is undefined. Create appropriate text regions in MathCad to explain what you are doing
at each step and why you are doing it. While the MathCad work is essential, you also have to
include enough explanation to make it VERY clear what you are doing, and must use appropriate
mathematical language. HINT: You can look back at your yellow sheets and follow through some
of my explanations to get a sense of what I am looking for. Also, be aware that MathCad
sometimes shows extraneous solutions when you use the solve feature, so make sure you are
thinking about what you are seeing. If you see evidence of an extraneous solution, make sure you
address why you realize it is extraneous.
b. (12 points) For each point where the function is undefined, use a similar process to the one laid
out on your yellow sheets to create appropriate tables in MathCad so that you can numerically
explore the functions behavior. Your tables MUST follow the standards that were set in lab – i.e.
no scientific notation, appropriate number of decimal places, appropriately aligned. Then verbally
explain what your tables represent, and what they help you determine. Finally capture the ideas
using appropriate limit notation, and explain what your notation tells you about the graphical
behavior you expect to see.
c. (10 points) Create appropriate tables that allow you to explore “tail” behavior of the function.
Again, verbally explain what your tables represent and what they help you determine. Finally
capture the ideas using appropriate limit notation, and explain what your notation tells you about
the graphical behavior you expect to see.
d. (6 points) Graph the function in a view window that allows you to clearly see all relevant function
behavior. Make sure you adjust your scaling so that it is easy to “read off” from the graph where
important graph behavior occurs. You MUST change the scaling on your graph so that is is
relatively easy to identify where the x and y intercepts occur. You MUST enlarge your graph.
2. (10 points) Show clear work with MathCad, and explain your thought process to numerically find the x
intercepts of h(x) x 4 5x 3 4x 5 . Make sure you show a complete graph.