MATH 021 UNIT 2 HOMEWORK ASSIGNMENTS

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1 MATH 021 UNIT 2 HOMEWORK ASSIGNMENTS General Instructions You will notice that most of the homework assignments for a section have more than one part. Usually, the part (A) questions ask for explanations, definitions, or examples. The purpose of these questions is to be sure you understand the vocabulary, ideas, and procedures of the section before you go on to problems. The part (B) questions are usually from the textbook. If there are other parts, they may be additional needed practice, as some of the topics in the course are not covered in the textbook. Some of the problems in the Unit 2 Homework Assignments review prerequisite material. If you need more review of these topics, see your instructor or go to the Math Lab for help. Do ALL your homework in your notebook or loose-leaf binder. Be sure to label each question. Be sure to read the directions very carefully, since you are often asked to do more than one thing in a problem. Be sure to write out all your work, since method is as important as getting the correct answer. The answers to the odd-numbered problems are in the back of the book, beginning on page A-11. The answers to the even-numbered problems and the extra questions (usually A or C) in this handout are all included at the end of this handout. If you have difficulty with a problem, mark the problem and write a note in the margin about your difficulty. In this way, when you go over homework in class, you can be ready with your questions. CHAPTER 3 Solving Equations Part III Section 3.4 Solving Equations with Algebraic Notation, Part 2 Text: Read pages B. Exercises 3.4, pages : 21, 22, 23, 24, 31, 32, 33, 34 Chapter 3 Review, page 184: 23 28, all Solve each of the following equations and show your check

2 Solving Equations Part IV Section 3.4 Solving Equations with Algebraic Notation, Part 2 Section 4.2 Proportions and Proportional Reasoning Answer these questions. 1. What algebraic steps do we use in solving an equation containing a fraction (for example )? 2. What algebraic steps might you use in solving an equation containing both a fraction and parentheses (for example )? For the following four questions, use the properties of equations to write a simpler equivalent equation for each equation below. Then explain what you did to get to the equivalent equation. Finally, solve the equation. 3. Hint: Divide each term by 1, Hint: Multiply each term by Hint: Multiply every term by 21, the LCD of all the fractions B. Exercises 3.3 pages 155: 19, 23, 29 Exercises 3.4 pages 165: all, solve algebraically; all, solve algebraically Text: Read pages Answer these questions. 1. What is a proportion? How can you tell if a proportion is a true statement? 2. Explain how to solve a proportion. Illustrate with an example. D. Exercises 4.2, pages : odd, odd Section 2.6 Inequalities, Intervals, and Line Graphs Section 3.5 Solving Linear Inequalities in One Variable Text: Read pages and Answer these questions. 1. What is an inequality? 2. Explain how x < 3 and 3 > x are equivalent statements. 2

3 3. Describe the effect on 3 < 4 of multiplying by Describe the effect on 3 < 4 of dividing by 2. B. Exercises 2.6, pages : 13 (omit b and h, ignore interval column), 17, 23, 27, 29 Exercises 3.5, pages : Omit write the solution set as an interval odd, 37, odd, 57, 59, 63 Section Formulas Text: Read pages B. Exercises 3.6, pages : 7, 9, 13, 15, 21, 25, odd, 37, odd, 53 CHAPTER 5 Section 5.1 Functions and Graphs Text: Read pages Answer these questions. 1. Look at each of the three tables labeled a), b) and c), given below. Each table represents a relationship between an input and an output variable. Decide which tables represent functions and which do not represent functions. Give a reason for each choice. a. Input Ouput b. Input Output c. Input Output What is meant by the domain of a function? 3. You go to the fruit stand to buy apples. The input is the number of pounds, p, of apples. The output is the cost, The cost is a function of the number of pounds of apples you buy. a. Write this relationship between pounds and cost, using function notation. b. means that the cost of pounds of apples is. c. If the cost is $4.52 for 3.5 pounds of apples, write this fact using function notation. 3

4 4. The equation can be used to find the approximate human age,, that corresponds to a dog's age, x. (This is true for dogs whose age is years, according to Simon & Schuster's Guide to Dogs.) a. Explain what means in the context of this problem? b. Evaluate. Explain the meaning of your answer in the context of this problem. 5. Explain how to find for the function. 6. Explain how the vertical line test identifies the graph of a function. 7. Sketch the graph of a function whose domain is the real numbers between 0 and 6, inclusive. 8. Use the graph of below to answer these questions: a. What is? b. What is x if? 9. Use the table at the right to answer these questions: a. What is? b. What is x if? x

5 B. Exercises 5.1, pages : 3, 9, 15, 25, 27, 33, 39, 41, Use to answer the following questions. a. Find. b. What is x if? c. Explain the difference between the problems in part a. and b. d. What is x if? e. Solve for x if? f. Solve for x if? 2. Use to answer the following questions. a. Find. b. What is x if? c. Solve for x if? d. Solve for x if? e. Explain why you can t answer Find. f. Find. Section 5.2 Linear Functions: Slope and Rate of Change Text: Read pages Answer these questions. 1. Explain in your own words what slope of a line means. 2. Write the formula for finding the slope of a line given two points on the line. Explain clearly what each letter in your formula represents. 3. What do the symbols Δy and Δx mean? 4. Explain how to tell from a graph if a line has positive slope. 5. Do horizontal lines have a slope? Explain. 6. Do vertical lines have a slope? Explain. 7. Explain how to find the slope of a line given two ordered pairs. 8. Does the slope of a line depend on the two points you choose? B. Exercises 5.2, pages : 1, 3. For problems 7, 9, 11, 14, 15, follow the instructions in the text and also state whether the graph of the line is rising, falling, vertical, or horizontal. Do problems 17, 19, 21, 29, 35, 37, 39, 40. Chapter 3 Review, pages : 27, 29, 47, 55, 69, 77 5

6 Section 5.3 Linear Functions: Intercepts and Slope Part I Text: Read pages , (Horizontal and Vertical Lines). Answer these questions: 1. What is a y-intercept? If you have an equation in x and y, how would you find the y- intercept? 2. What is an x-intercept? If you have an equation in x and y, how would you find the x- intercept? 3. What is the equation of a horizontal line whose y-intercept is b? 4. What is the equation of a vertical line whose x-intercept is a? B. Exercises 5.3, pages : 3, 5, 7, 31, 33, 43, 45, 47, 49, 59 Exercises 5.4, pages : 37, 41, 42, 43 Answer these questions: 1. For the graph on the right, a) Find the slope of the line. (Note the scale!) b) What is the y-intercept? c) What is the x-intercept? 2. Based the input-output table on the right, find a) f(0). b) x when f(x) = 0. c) The answer to part a) gives the intercept and the answer to part b) gives the intercept. x f(x) Section 5.3 Linear Functions: Intercepts and Slope Part II Text: Read pages , pages (through Practice 1 only). Answer these questions: 1. What is a linear function? Give an example. 2. Suppose the equation of a line is given as 2x 3y = 12. Is the slope of the line 2? Explain. 6

7 B. Exercises 5.3, page 287: 9, 11, 15, 17, 21 Exercises 5.4, pages : 1, 3, 7, 33, 35, 53, 55, 57, 59 Answer these questions: 1. If f(x) = 6x + 5 a) Find f( 2). Write the ordered pair that you just found. b) Find f(0). Write the ordered pair that you just found. c) Find x if f (x) = 0. Write the ordered pair that you just found. 2. Use graph paper to draw a line with slope 2 and y-intercept 5. Label four points on the line. 3. For the graph on the right, a) Find the slope. b) Find the y-intercept. c) Write the equation of this line. D. Chapter 5 Review, pages : 13, 31 34, 41, 55, 59 Section 5.4 Linear Equations Text: Read pages 291 (after Practice 1) 295 (through Example 8 only). B. Exercises 5.4, pages : 9, 11, 15, 17, 21, 23, 25, 39, 45, 47, 49, 51 Chapter 5 Review Exercises, page 313: 94 Answer these questions: 1. a. What are the slope and y-intercept of the linear equation y = x +5? b. Use the y-intercept and slope to graph on graph paper, the line y = x Graph a line on graph paper which passes through ( 2, 1) and has slope. 7

8 3. The table on the right shows the value remaining on a card that was purchased at the Library, which can be used to make copies. a. Find the slope of the line. Use correct units. b. Explain the meaning of the slope of the line. c. Find the y-intercept. d. Explain the meaning of the y-intercept. Copies Value Remaining 0 $ $ $ $ Explain why the pairs of lines are parallel or not? y = 4x 3 and y = x 4 5. a. Write the equation of the line that is parallel to and passes through the point (0, 4). b. Write the equation of the line parallel to y = 3x 2 that passes through the point ( 2, 5). SOLUTIONS Section 3.4 B Chapter 3 Review Section 3.4, Multiply both sides of the equation by the least common denominator. 2. First, multiply both sides of the equation by the least common denominator. Next, distribute. Subtract the constant from both sides, and finally divide by the coefficient of x. Check your solution in the original equation

9 6. Multiply each term by 24, the LCD of all the fractions. 7. Multiply both sides of the equation by 10: B A proportion is an equation formed by two equal ratios. The proportion is true if the cross-products are equal. 2. In general, solve a proportion by crossmultiplying and solving the resultant equation. Section 2.6, An inequality is a statement that one quantity is greater than or less than another quantity. 2. The statement x < 3 describes all numbers less than 3. The statement 3 > x says that 3 is bigger than all included numbers, so it is an equivalent statement. 3. When you multiply the inequality by 2, you must change the sense of the inequality. The inequality becomes 6 > When you divide the inequality by 2, you must change the sense of the inequality. The inequality becomes 1.5 > 2. Section a and c are functions: for each x there is exactly one y or you can say that the input values are not repeated; b is not a function because the inputs 1 and 3 are repeated so for each of those input values, there are two output values. 2. The domain of a function is the set of all input values. 3. a. b. 5 pounds of apples is $6.45 c. 4. a. A dog that has been living 7 years is approximately 50 years old in human age. b.. A 12 year old dog is about 75 years old in human age. 5. Substitute a for x and evaluate the function to find y. 6. If a vertical line cuts the graph in more than one place, then, at that x-value, there is more than one y-value, so the graph is not a function. 7. Many possible graphs, but the graph should not go to the left of 0 or to the right of a. 25 b a. 4 b a., b., c. In part a you are given an input of 3 and asked to find the corresponding output. In part b you are given an output of 3 and asked to find the corresponding input., d., e., f.. 2. a., b., c., d., e. The function s name is not, f.. Section Slope is a measure of the steepness and direction of a line. 2. ; m is the slope, is one point and is the other point on the line. 3. means the amount of change in y (vertical change); means the amount of change in x (horizontal change). 4. The slope is positive if the line rises from left to right. 5. The slope of a horizontal line is 0 since the change in y is Vertical lines do not have a slope since the change in x is 0, making the denominator of the fraction 0. Thus the number is undefined. 7. Find the difference in the y-values and divide by the difference in the x-values. Be sure to use the same order of subtraction for both. 8. No. It will be the same no matter which points are chosen. 17

10 B. 14. The slope is undefined; the line is vertical. 40. The slope is 10; the units are thousand dollars per year. This means that salary increases $10,000 per year of experience. Section 5.3 Part I 1. The y-intercept is the point where a graph crosses the vertical (y) axis. To find it, set x = 0 and solve for y. 2. An x-intercept is a point where a graph crosses the horizontal (x) axis. To find it, set y = 0 and solve for x. Section 5.3 Part II 1. Any association between x and y that can be written in the form y = mx + b 2. No. The equation is not written in y = mx + b form. 2. Select four points from the following: ( 3, 1), (-2,1), ( 1,3), (0,5), (1,7) 3. y = b. 4. x = a. B. 42. line AB 1. a. 5 b. (0, 10) c. ( 2,0) 2. a. 4 b. 2 c. vertical, horizontal 1. a. 7. ( 2, 7) b. 5. (0, 5) c.. g The rental costs $0.89 per mile. h. y = 0.89x i. about ( 22.5,0). Has no practical meaning. 1. a. m = 2/3, b = 5 b. 3. a. 1/10 b. 1 D. 32. e 34. c c. y = 1/10 x 1 Section 5.4 B. 94. a. miles b. cost c. yes d. $31.12 e. about 41.5 f. (0,19.99). Initial cost of the rental is $

11 2. 4. Not parallel because the first has a slope of 4 while the second has a slope of ¼. 5. a. y = 2x + 4 b. y = 3x 3. a. $ 0.25/copy b. Each copy costs $0.25. c. 15 d. The initial value of the card was $