Lab. 1: Pre-Calculus LAB Distance, Midpoint, Slope, Linear Function

1) Use Maple to compute the following:

a) Use the slope command in Maple to find the slope of the following: 3x + 2y = 6. Graph and estimate the y-intercept.

b) Given the following (-2, -5) and (5,8) compute the distance, midpoint, and the slope in Maple.

c) Given the following (-6,3) and (3,-5) compute the distance, midpoint, and the slope in Maple

d) Solve the following algebraically and graphically in Maple: x + 4 = 5y - 3 4y + 2x = 0

e) Solve the following algebraically and graphically in Maple: 3x + 3y = 3
4x + 2y = 8/3 Comments on your results on part d) and e) ( make sure that they agree)

2) A shoe manufacturer determines that the annual cost of making x pairs of one type of shoe is $30 per pair plus $100,000 in fixed overhead costs. Each pair of shoes that is manufactured is sold wholesale for $50.

a) Find the equations that model Revenue and cost and graph each equation on the same x-y coordinate systems.

b) Use the graph to find how many pairs of shoes that must be sold in order for the manufacturer to break even.

c) Use the graph to estimate the cost of manufacturing 8000 pairs of shoes. Estimate the profit.

3) The following table lists percentages of women in state legislature for past years.

a) Make a scatter plot of the data

b) Use Maple to find the least-squares regression line that models this data. Graph both the data and the model on the same x-y axis.

c) Interpret the slope

d) Using this model in part, estimate the percentage of women in state legislator in 2001.

4) It is possible for archeologists to estimate the height of an adult based only on the length of the humerus, a bone located between the elbow and the shoulder. The approximate relationship between the height y of an individual and the length x of the humerus is shown in the table for both males and females. All measurements are recorded in inches.

a) Make a scatter plot for both sexes.

b) Use Maple to find the least-squares regression lines for females and males respectively and graph each model and the data on the same x-y axis

c) Suppose part of a broken humerus is estimated to be between 9.7 and 10.1 inches in length. If the sex is not known, use both models to approximate the range for the height of an individual of each sex.

5) The following data in the table represents the apparent temperature versus the relative humidity in % in a room whose actual temperature is 75° F.

a) Make a scatter plot

b) Use Maple to find the least-squares regression line that models this data. Graph both the data and the model on the same x-y axis.

c) If the relative humidity is 75%, estimate the apparent room temperature. Top

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Lab. 2: Pre-Calculus LAB Piecewise functions, Quadratic Functions, evaluate functions, Transformations

1) Given:

a) Graph f(x) and y1=f(x+2) on the same x-y axes and describe their relationship.
b) Graph f(x) and y2=f(x-4) on the same x-y axes and describe their relationship.
c) Graph f(x) and y3=f(x) + 4 on the same x-y axes and describe their relationship.
d) Graph f(x) and y4=f(x) - 2 on the same x-y axes and describe their relationship.
e) Graph f(x) and y4=-3*f(x) on the same x-y axes and describe their relationship

2) Graph the following function

:

3) Given :

a) Graph Approximate any local extrema
b) Approximate any absolute extrema
c) Determine the x-intervals where h is increasing or decreasing

4) Let :

, and

a) find f + g
b) find f - g
c) find f * g
d) find (f+g)(2)
e) find (g/f)(-1/2)
f) find f(g(x)) and g(f(x)), graph and compare both functions.

5) The height Y (in feet) of a ball thrown by a child is given by:

where x is the horizontal distance (in feet) from where the ball is thrown

a) Graph Y
b) How high was the ball when it left the child's hand?
c) How high was the ball when it was at its maximum height?
d) How far from the child did the ball strike the ground?

6) A golf course company has determined that the daily per unit cost C of manufacturing x additional golf clubs may be expressed by the quadratic function:

Graph C
How many clubs should be manufactured to minimize the additional cost per club?
At this level of production, what is the additional cost per club?

7) The height H of a ball (in feet) thrown in the air is given as a function of time t (in seconds) by:

a) Find the initial height of the ball.
b) Determine the time at which height is maximum.
c) What is the maximum height of the ball?

8) The price p and the quantity x sold of a certain product obey the demand equation:

x = -20p + 500, 0 p 25

If Revenue, R(x), is given by: R(x) = x*p

a) Graph R(x)
b) What is the revenue when 20 units are sold?
c) What quantity x maximizes revenue?
d) What is the maximum revenue?
e) What price should the company charge to maximize revenue? Top

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Lab. 3: Composition, Asymptotes & One-to-One Functions

1) Graph each function and Identify the asymptotes. Find the domain and range for each function

a)

b)

c)

d)

e)

2)

and

a) find f(g(x)) and graph
b) find g(f(x)) and graph
c) Identify the asymptotes if possible

3) y=f(x) = graph and determine whether y is one-to-one. (Explain)

b) If f(x) is not one-to-one then find domain over which f(x) is one-to-one.
c) Use Maple to find the inverse of f(x) for the restricted domain found in part b).
d) Graph both f(x) and its inverse.

4) Find the inverse of the following and state the domain (Hint: solve for x):

a)

b)

c)

d) Graph each function with its inverse on the same x-y coordinate systems.

5) Graph the following function and its inverse on the same x-y axes.

What general conclusion can you draw when graphing a function and its inverse? Top

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Lab. 4 & 5: Exponential & Logarithm

Part I :

1) Graph and Compare the following:

a) and

b) and

c) and

d) and

e) and

2) Graph the following functions:

and Describe the relation between p and q Find the domain and the range.

3) Graph the following functions: and

a) Describe the difference between f and g

b) Find the domain and the range

4) Solve the following using graphical method:

a)

b)

5) There is a mathematical relation between an airplane's weight x and the runway length required at takeoff. For some airplanes the minimum runway length in thousands of feet may be modeled by : , where x is measured in thousands of pounds.

a) Graph L

b) Estimate (graphically) and evaluate (algebraically) the length of the runway when the weight is 10,000 and 100000 pounds.

c) Does the length of the runway from part b) increase by a factor of 10?

d) Generalize your answer for part b) and c)

Part II

Exponential & Logarithm (Applications)

1) As age increases, so does the likelihood of coronary heart disease (CHD). The fraction of people x years old with some CHD is modeled by:

a) Graph f(x)

b) Estimate (graphically) and Evaluate (algebraically) f(25) and f(65). Compare your estimation with your algebraic results.

c) Interpret the results from part b)

d) Estimate at what age does this likelihood equal 50%?

2)

A) Find an exponential model for the federal debt, based on the data in the table for Accumulated Gross Federal Debt. Let x = 0 correspond to 1960.

B) Plot both the data points and the model on the same x-y axis. Describe how well the model matches the data points.

C) Use the model to predict the federal debt in 2002

3) The Drug Medication formula: can be used to find the number of milligrams D of a certain drug that is in a patient's bloodstream h hours after the drug has been administered. When the number of milligrams reaches 2, the drug is to be administered again. Plot the function D and estimate the time between injections. (Brain teaser :) After how many hours will the third injection occur?

4) Stronium-90 is a radioactive material that decay according to the following function: , A0 is the initial amount. A) What is the half-life of stronium-90? B) Suppose you start with 50 milligrams, graph the function and use the graph to convince yourself that part A) is the correct answer. C) Use the graph to estimate when 7 milligrams will remain. D) Find the exact value for part C)

5) The table shows the number of babies born as twins, triplets, quadruplets, etc, in recent years.

a) Make a scattered plot of the data.

b) Use the following models and plot each on the same x-y axis as the data points

c) Which model do you think is a better predictor over the long run?

d) Use that model to predict the number of multiple births in 2005

6) A $1000 is invested at a continuously compounding rate of 6% annually. A) Estimate and calculate exactly how long it takes for that investment to double. Compare your estimate with your exact value. B) How long it takes that same investment to quadruple. (show both estimation and exact calculation.). C) When will the investment reach $12,000?

7) The population of the U.S. is measured every 10 years by the Census Bureau. The following is a partial list of the census figures.

a) Make a scatter plot of the data

b) Find a formula that describes the growth of the population in the US

c) Plot both the formula and the data on the same x-y-axis

d) Use the formula to predict the population of the US in 2005 Top

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