A) a Summary with Important Characteristics for Each of the Functions Studied in Class

Portfolio

This semester you will be required to keep a portfolio. In the portfolio you will include

a) A summary with important characteristics for each of the functions studied in class.

b) The complete solution of selected applications (word problems) of the different functions

You should also include the following:

For each of the functions studied in class you have to write a summary

Including the graph, domain, range, and important characteristics of the

Instructions for Completing the Word Problems which are in my web page

Save the document in your computer.

Delete everything except for the word problems.

Save the document with one word problem per page.

Print all pages, and show work on those papers.

Objective:

Develop the ability to solve word problems, and to write mathematically.

You have to show all algebraic steps in order to get credit.

This will develop your ability to write mathematically.

Write interpretations using whole sentences. NEATNESS is very important.

Why using a rubric?

Using a rubric to grade your papers

-allows assessment to be more objective and consistent

-clearly shows how your work will be evaluated and what is expected

Word Problems that should be included in your portfolio

Section 1.6

Measuring Temperature

The relationship between Celsius (ºC) and Fahrenheit (ºF) degrees of measuring temperature is linear.

a)Write an equation for degree Celsius in terms of degrees Fahrenheit if 0ºC corresponds to 32ºF and 100ºC corresponds to 212ºF.

b)Use the equation to find the Celsius measure of 70 º F. Solve algebraically.

c)Use the equation to find the Fahrenheit measure of 30º C. Solve algebraically.

d)Use your calculator to sketch the graph. Label axes with symbols and words. Indicate window values used.

e)Use your calculator to answer question (b). Use the 2nd TRACE[CALC] feature or the 2nd GRAPH[TABLE] feature.

f)Answer question (c) using a graph. Show how you do this.

g)Write an equation for degree Fahrenheit in terms of degrees Celsius

Section 2.1

Effect of Gravity on Jupiter

If a rock falls from a height of 20 meters on the planet Jupiter, its height H (in meters) after x seconds is approximately

H(x) = 20 – 13 x^2

a)Use the calculator to graph. Label axes with symbols and words. Indicate window values used.

b)What is the height of the rock one second after it was released? Solve algebraically.

c)What is the height of the rock 1.1 seconds after it was released? Explain how you solve with the CALCULATE menu.

d)What is the height of the rock 1.2 seconds after it was released? Explain how you solve with the TABLE feature, ASK mode.

e)When is the height of the rock 15 meters? Solve algebraically.

f)When is the height of the rock 10 meters? Explain and show how you solve graphically.

g)When does the rock hit the ground? Solve algebraically, then explain and show how you solve graphically.

Section 2.3

Minimizing the Volume of a Box

An open box with a square base is to be made from a square piece of cardboard 30 inches on a side by cutting out a square from each corner and turning up the sides.

a)Write an expression for the volume of the box V, as a function of the length x of the side of the square cut from each corner.

b)Graph the function. Label axes with symbols and words. Indicate window values used.

c)Use your calculator to find the dimensions of the box that maximize the volume.

d)What is the largest volume? Label maximum point in graph.

Section 2.7

Installing Cable TV

Similar to problem # 19, page 164 (notice that numbers have been changed)

Metro Media Cable is asked to provide service to a customer whose house is located 3 miles from the road along which the cable is buried. The nearest connection box for the cable is located 6 miles down the road (see figure on # 19, page 164)

a)If the installation cost is $110 per mile along the road and $140 per mile off the road, express the total cost C of installation as a function of the distance x (in miles) from the connection box to the point where the cable installation turns off the road. Give the domain of this function.

b)Compute the cost if x = 1 mile. Do algebraically.

c)Compute the cost if x = 3 miles. Use the TABLE feature, ASK mode.

d)Graph the function C = C(x). Label axes with symbols and words. Indicate window values used.

e)Create a TABLE starting at x = 0 and with an increment of 0.1. (Use 2ndTBLSET[WINDOW]). Use the table to answer which value of x results in the minimum cost? What is the minimum cost?

f)Now use the graph and the CALCULATE menu to answer part (e). Label in the graph.

Section 3.1

Enclosing the Most Area with a Fence

A farmer with $12,000 meters of fencing wants to enclose a rectangular field and then divide it into three plots with a fence parallel to one of the sides. What is the largest area that can be enclosed? What are the dimensions of the rectangle with largest area?

a)Solve algebraically.

b)Graph the function. Label axes with symbols and words. Indicate window values used. Label important features in the graph.

c)Explain how you solve by using the graph.

Section 3.5

Population model

Do problem # 46, page 235.

Each part has to be solved algebraically.

Explain how to solve each part with the calculator.