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Quiz 2

1 .       Which of the given graphs is not the graph of a function, y = f(x)?


2 .       Find the domain of 1m2q2_1.gif and express it in interval notation. 

3 .       Given the function 1m2q3_1.gif, find the quotient 1m2q3_2.gif; simplify your answer. 

4 .       Body mass index (BMI) relates body weight to health risks associated with being overweight. To figure a person's BMI you need to perform the following calculations:

(a) multiply weight (in pounds) by 0.45
(b) multiply height (in inches) by 0.025
(c) square the result in step (b)
(d) divide the result in step (a) by the result in step (c).

Let B denote the BMI of a woman weighing 150 pounds, write an equation describing B as a function of h, where h represents the woman's height in inches. (Source: The Mayo Clinic Healthy Weight Plan) 

5 .       The graph of a function y = f(x) is obtained by applying to the graph of y = |x| first a vertical shift 3 units upward and then a reflect about the x - axis. Find an equation describing the function f(x). 

6 .       Toni's is a small family business which imports gourmet food from Italy. The data in the table give the prices, per package, of a first quality Italian pasta sold at Toni's. Write a formula for the function C(x) expressing the cost of buying x packages of pasta at Toni's.

Prices at Toni's
# of packages of pasta Up to 4 More than 4 and up to 12More than 12
Price p in dollars1.801.601.30

7 .       State the geometric transformations, in the correct order, which need to be applied to the graph of 1m2q7_1.gif, to obtain the graph of 1m2q7_2.gif

8 .       The graph of a linear function y = f(x) passes through the points (1,1) and (-1,5); find an equation for f(x) and find the x and y intercepts of this function. 

9 .       You want to invest $2,500 and you are considering two investment plans, plan A and plan B. Let A = A(t) and B = B(t) be the functions representing, respectively, your investment amount for plan A and plan B after t years. Indicate which one, if any, is a linear function and state its slope and y intercept.

t (years) 0 1 2 5 10
A(t) (years) 2,500 2,700 2,900 3,500 4,500
A(t) (years) 2,500 2,675 2,862 3,506 4,918

10 .       Gabriella purchased a new vacuum cleaner at a price of $600 to use in her house cleaning business. For tax purposes, its value is considered to depreciate linearly to $50 over a 5 year period. If V represents the value of the vacuum cleaner, in dollars, and t represents time, in years after the purchase, find an equation containing V and t

11 .       The equation 1m2q11_1.gif is used to convert a temperature measure from degrees Fahrenheit (F) to degrees Celsius (C). It is a hot summer day, you are at home and you feel comfortable at a temperature of 25 degrees Celsius or below; if the values on your thermostat (which controls the air conditioning unit) are expressed in degrees Fahrenheit, at what level should you set it? 

12 .       Given the function 1m2q12_1.gif, find its maximum or minimum and the value of x at which it occurs. 

13 .       Solve the given inequality to two decimal places:


14 .       A cleaning company is advertising a particular type of service for $42.00. If the cost for providing that service is given by the functions C(x) = 200 + 20x (where x is the number of services provided per weel and C(x) is the corresponding cost in dollars), and if the price-demand equation has been estimated to be p = 70 -0.7x, should the company increase or decrease the charge for the service, in order to maximize profit? Choose the best of the following: 

15 .       State the geometric transformations which can be applied to the graph 1m2q15_1.gif to obtain the graph of 1m2q15_2.gif. [Hint]

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