M-Sci Math 1 July 9, 2018 page 1

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1 M-Sci Math 1 July 9, 2018 page 1 1. Below are some tables of values of three functions f, g, and h. Determine if each function could be a linear function or if the function must not be a linear function. x a. f(x) b. t g(t) c. y h(y) Link s catering company provides food for cat parties and important cat business meetings. To help increase his sales, Link offers special discounts for cats placing large food orders. a. For small orders, Link sells tuna at a price of $0.30 per ounce. If the customer purchases more than 50 ounces of tuna, Link charges $0.30 per ounce for the first 50 ounces and $0.25 per ounce for any tuna beyond the first 50 ounces. Let T (q) be the total cost of purchasing q ounces of tuna from Link. Find a formula for T (q). b. Link decides to try a new pricing scheme for chicken. For orders less than 100 ounces, Link will charge $0.25 per ounce. If the customer orders more than 100 ounces, he will decrease the price per ounce for the entire order by $0.01 for every additional 5 ounces the customer purchases. For example, if a customer purchases 110 ounces of chicken, Link will charge $0.23 per ounce for the whole order. Link s kitchen space is limited, so he can provide a maximum of 200 ounces of chicken per order. Let C(q) be the total cost of purchasing q ounces of chicken from Link. Find a formula for C(q).

2 M-Sci Math 1 July 9, 2018 page 2 3. Below is a graph of w = h(z) for some function h. 4 w w = h(z) z Evaluate each of the following quantities. a. h( 1) = b. h(h( 2)) = c. h 1 ( 1) = d. h 1 (0) = e. h 1 (2h(0)) = f. h(h 1 (3)) = 4. Suppose that b = f(a), with f(a) = 10a 8. a. Evaluate f 1 (22). b. Find a formula for f 1 (b). c. Find and simplify a formula for f (f(a)). d. Find and simplify a formula for f ( f 1 (b) ).

3 M-Sci Math 1 July 9, 2018 page 3 5. Below is some information about three invertible functions f, g, and h. x f(x) g(x) = 24 6 x y y = h(x) x Use the information above to evaluate each of the following expressions. a. g(f(2)) = e. f 1 (h( 4)) = b. f 1 (4) = c. h(0) = f. g 1 (8) = g. h ( 43 ) f( 2) = d. h 1 (0) = h. g (f (h(3) + 1)) = 6. Consider the function M defined by M(y) = 5 + y y 8. a. Evaluate M 1 (10). b. Find a formula for M 1 (z).

4 Math 105 / Exam 1 (October 10, 2011) page [10 points] In this problem, we consider two functions: W (s) is the wind chill 1 (in degrees Fahrenheit) when the temperature is 30 degrees Fahrenheit and the wind speed is s mph (miles per hour). B(c) is the time (in minutes) it takes to develop frostbite on exposed skin when the wind chill is c degrees Fahrenheit. Assume both W and B are invertible. Fill in each blank below with one of the possible answers given below. Note that a given answer may be used in more than one blank, and that not all possible answers will be used. Possible Answers: 20 W (20) B(20) W(20)+B(20) W 1 (20) B 1 (20) W (B(20)) B(W (20)) W 1 (B 1 (20)) B 1 (W 1 (20)) W (B 1 (20)) B(W 1 (20)) *Assume throughout this problem that the temperature is 30 degrees Fahrenheit.* a. [2 points] If the wind chill is degrees Fahrenheit, the wind speed is 20 mph. b. [2 points] When the wind speed is 20 mph, exposed skin will develop frostbite in minutes. c. [2 points] If the wind chill is 20 degrees Fahrenheit, then the wind speed is mph. d. [2 points] If the wind chill is 20 degrees Fahrenheit, then it will take exposed skin minutes to develop frostbite. e. [2 points] When the wind chill is B 1 (20) degrees Fahrenheit, exposed skin will develop frostbite in minutes. 1 Note that wind chill is the temperature it feels like.

5 Math 105 / Exam 2 (March 20, 2012) page [10 points] Ivanka is a student at a nearby college. Let C(h) be the total tuition, in thousands of dollars, the college charges her if she takes h credit hours, and let a be the average number of credit hours students take at the college. For each of the following, pick the one expression from the list of Answer Choices that best represents the described quantity. Clearly write the capital letter of your choice on the answer blank provided. Answer Choices A. C(3) B. C 1 (3) C. C(a) D. C 1 (a) E. C(a + 3) F. C(a) + 3 G. C(a 3) H. C(a) 3 I. 3C(a) J. C(3a) K. 3C 1 (a) L. C 1 (a)/3 M. C(a)/3 N. C(a/3) O. C 1 (a/3) P. C 1 (3a) Q. 3C(C(a)) R. C(3C 1 (a)) S. C 1 (3C(a)) T. C 1 (C(3a)) a. [2 points] Ivanka s tuition (in thousands of dollars) if she takes a total of 3 credit hours b. [2 points] Ivanka s total tuition (in thousands of dollars) if she takes 3 credit hours more than average c. [2 points] Ivanka s tuition (in thousands of dollars) if she takes one third the average number of credit hours d. [2 points] The amount (in thousands of dollars) that Ivanka pays for tuition if she takes the average number of credit hours but has a scholarship that covers three thousand dollars of her tuition e. [2 points] The number of credit hours Ivanka takes if her total tuition is three times as much as the tuition for taking the average number of credit hours

6 Math 105 / Final (December 17, 2013) page 7 7. [8 points] Freckles and Comet are cats in the same household. Consider the functions F, C, and D which are defined as follows: F (m) is the number of ounces of food that Freckles eats in month m. C(m) is the number of ounces of food that Comet eats in month m. D(q) is the cost of buying q cans of cat food at a time when there are no sale prices. Assume that D is invertible. For each of questions below, circle the one best answer from among the options provided. If none of the options are correct, circle none of these. Please note: To receive credit, you must clearly circle your choices. (Circle the entire answer. If there is any ambiguity in your answer, you will not receive credit.) a. [1 point] What is the total number of ounces of food that Freckles and Comet eat in month m? D(m) + C(m) F (m) + C(m) F (C(m)) C(F (m)) none of these b. [2 points] Suppose that there are 3 ounces of food per can. What is the total cost of the food Freckles eats in month 4? ( ) D(4) F (4) 3D(4) D(3F (4)) D none of these 3 3 c. [1 point] Let A(q) be the average cost per can of buying q cans of cat food. Which of the following is a formula for A(q)? D 1 (q) q D(q) F (q) + C(q) 2 D(q) q none of these d. [1 point] When there are no sale prices, how many cans of cat food can be purchased at a time for $20? D(20) D 1 (20) 20D 1 (q) 1 D(20) none of these e. [2 points] Suppose that Comet eats at least twice as much food each month as Freckles eats. Which one of the following inequalities most accurately describes this relationship? C(m) 2F (m) C(m) 2F (m) 2C(m) F (m) 2C(m) F (m) f. [1 point] If cat food goes on sale for 40% off its regular price, what is the cost of buying 20 cans of cat food at one time? 0.6D(20) 1.4D(20) 0.4D(20) D(8) none of these