Practice Problems. 1. The age and weights of six cats are given in the following table:
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1 1. The age and weights of six cats are given in the following table: Age (in years) A Weight (in pounds) - W a. Identify the input and output quantities and their associated variables. b. Write the given data as a set of ordered pairs. c. Is Weight a function of Age for the six cats? Why or why not? d. In the general population, is Weight a function of Age (i.e. for every age (input) is there one and only one value for the weight (output)?) 2. Explain your choice for each of the following. Remember when the word function is used, it is in a purely MATHEMATICAL sense not in an everyday sense. a. Is how far you ve driven on a road trip a function of how long you ve been driving? b. Is the number of movies a person watches in a year a function of their age? Scottsdale Community College Page 17 Intermediate Algebra
2 3. The table below shows 6 different possible functions. For each determine if it represents a function or why it fails as a function. Data Set Relationship 1 Relationship 2 x y OR x y x y OR x y Set of Ordered Pairs {(3, 1), (-2, 3), (0, 5), (3, 8), (5, 10)} {(0, 0), (1, 2), (2, -1), (3, 4), (4, 2)} Graph Scottsdale Community College Page 18 Intermediate Algebra
3 4. Suppose the number of pizzas you can make in an 8 hour day is determined by the function P(t) = 12t where P is the output (Pizzas made) and t is the input (Time in hours). a) Graph this function using your calculator. [Go to Y= and type 12x into the Y1 slot. Then, press WINDOW and enter xmin = 0, xmax =8, ymin = 0, and ymax=96 then press GRAPH]. Show a good graph in the space below. b) Use the Table feature of your graph and identify the first and last ordered pairs that are on the graph (based on the information above). [2 nd >Graph will take you to the table]. Include both ordered pairs and function notation. c) What is the INPUT quantity (including units) for this Name the smallest and largest possible input quantity then use this information to identify the PRACTICAL DOMAIN. d) What is the OUTPUT quantity (including units) for this Name the smallest and largest possible output quantity then use this information to identify the PRACTICAL RANGE. Scottsdale Community College Page 19 Intermediate Algebra
4 5. A local window washing company charges $0.50 per window plus a base fee of $20.00 per appointment. They can wash a maximum of 200 windows per appointment. a) Let C represent the total cost of an appointment and w represent the number of windows washed. Using correct and formal function notation, write a function that represents total cost as a function of windows washed. b) Identify the practical domain of this function by filling in the blanks below. Minimum windows washed w Maximum windows washed Practical Domain: w c) Identify the practical range of this function by filling in the blanks below. Minimum Cost C(w) Maximum Cost Practical Range: C(w) d) Enter the equation for C into the Y= part of your calculator. Then use the TABLE feature to complete the table below: w C (w) e) Use the TABLE to determine the value of C(50). Circle the appropriate column in the table. C(50) = f) Use the TABLE to determine w when C(w) = 45. Circle the appropriate column. When C(w) = 45, w = g) Use your FUNCTION from part a) to determine the value of w when C(w) = 45. Set up the equation, C(w) = 45 then solve for the value of w. Scottsdale Community College Page 20 Intermediate Algebra
5 6. For each of the functions below, evaluate f(2), f(-1), f(1+x), and f(-x): a) f(x) = -x + 6 b) f(x) = 14-2x c) f(x) = -2(x + 4) d) f(x) = 2x 2 + x - 2 Scottsdale Community College Page 21 Intermediate Algebra
6 7. Graph each of the following functions on your graphing calculator restricting the input window to Xmin = -5 and Xmax = 5 and draw an accurate sketch here [Go to Y= and type in the equation. Then go to Window and enter -5 for Xmin and 5 for Xmax. Leave Ymin at -10 and Ymax at 10]. For each graph, if we restrict the domain and range to the data visible in the window, indicate the practical domain and range. a) y = -x + 1 b) y = x 2 + 2x + 1 Practical Domain: Practical Range: Practical Domain: Practical Range: Scottsdale Community College Page 22 Intermediate Algebra
7 8. Find the practical domain and practical range for the graphs below then fill in the other blanks. Use proper INEQUALITY notation for your domain/range responses (as in Worked Example 3/Media Problem 5). Function F(x) Practical Domain: Practical Range: F(0) = When F(x) = 0, x = Function G(x) Practical Domain: Practical Range: G(0) = When G(x) = 0, x = or Scottsdale Community College Page 23 Intermediate Algebra
8 9. Given f(x) = 3x - 6, determine each of the following. Round to two decimals as appropriate. GIVEN INPUT FIND OUTPUT GIVEN OUTPUT FIND INPUT Find f(0) Find x if f(x) = 7 Find f(-2) Find x if f(x) = Given f(x) = -4x 2, compute each of the following. Round to two decimals as appropriate. GIVEN INPUT FIND OUTPUT GIVEN OUTPUT FIND INPUT Find f(2) Find x if f(x) = 7 Find f(-3) Find x if f(x) = The life expectancy for males in the United States can be modeled by the function L(x) = 0.27x , where L is the life expectancy and x is the number of years since a) Which letter, L or x is used for input? b) What does the INPUT represent? Include units. c) Which letter, L or x, is used for output? d) What does the OUTPUT represent? Include units. Scottsdale Community College Page 24 Intermediate Algebra
9 e) Draw a neat, labeled and accurate sketch of this graph in the space below. You may use the graphing feature of your calculator to help you (Y=). The recommended window is: x min=0, xmax = 120, ymin=0 and ymax = 100. Fill in the ordered pair table, and plot and label those points on your graph. x L f) What is the practical domain of L(x)? Use proper inequality notation. g) What is the practical range of L(x)? Use proper inequality notation. h) What is the life expectancy of a man born in Iowa in 1950? Hint: This is a GIVEN INPUT FIND OUTPUT question. Show your work!! i) If a man is expected to live to the age of 60, approximate the year he was born. (Round to one decimal place)? Hint: This is a GIVEN OUTPUT FIND INPUT question. Show your work!! Scottsdale Community College Page 25 Intermediate Algebra
10 Scottsdale Community College Page 26 Intermediate Algebra
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