Linear Function. Work through the steps below to create a linear function and use it to predict behavior.

Transcription

1 Name Instructor: INSTRUCTIONS: Work these problems in the space provided and turn in these pages along with your solutions to the section review problems. Check your answers using the key provided in the ILC. SUPPLEMENTAL EXERCISE FOR 2.5: Linear Function. Work through the steps below to create a linear function and use it to predict behavior. Basic Information: A VHS videocassette contains 800 feet of tape. In the long play (LP) mode, it plays 10 feet of tape every 3 minutes. The number of feet yet to be played (the number of feet remaining on the tape) depends on the length of time that the tape has been playing. In other words, the number of feet remaining on the tape is a function of the length of time the tape has been playing Step One: Complete the table of values. The first column gives the amount of elapsed time. Determine how many feet of tape remain on the tape after it has been playing for 30 minutes, 60 minutes, etc. Note that at time x = 0 all 800 feet of tape remain on the tape because no tape has been played. minutes played x Number of feet remaining y Step Two: Graph the data from the table. Indicate the appropriate scales on the horizontal and vertical axes and indicate what quantities the axes represent.

2 SUPPLEMENTAL EXERCISE FOR Linear Function: Page 2 of 7 Step Three: The graph in Step Two should be a straight line. If it is not, recalculate the values you put into the table and re-plot. Find an equation for the straight line and write it in slope-intercept form. What is the slope of the line? The slope represents the rate of change in the number of feet of tape played per minute. Step Four: The number of feet of tape remaining is a function of the amount of elapsed time. To represent this special relationship we use the function notation f x. Write the linear equation you found in Step Three using function notation: ( ) The input to this function is time x; the output is the number of feet y played. The set of all possible input values for x is called the domain of the function. What is the domain for this function (think about what x represents)? The set of all possible output values y is called the range of the function. What is the range for this function (think about what y represents)? Step Five: We can use the function to find how many feet of tape will have been played after some amount of time has elapsed. What is f ( 75)? Interpret your answer in the context of this problem. What is f ( 100)? Interpret your answer in the context of this problem.

3 Page 3 of 7 SUPPLEMENTAL EXERCISE FOR Linear Function, Step Five: We can also use the function to determine how much time has elapsed if a certain amount of tape remains. What is the value of x if f ( x ) = 160? Interpret your answer in the context of this problem. SUPPLEMENTAL EXERCISE FOR 2.6: Translation of Graphs. For each problem below, identify the basic function being translated and the type of translation (vertical, horizontal or reflection). Then sketch the graph of the basic function along with the graph of the translated function. Label each graph with its appropriate function. Lastly, find the domain and range of the translated function. ( ) = x 2 ( ) ( ) 2 g x g x = x 3 + 1

4 Page 4 of 7 3 ( ) x g x = + 2 SUPPLEMENTAL EXERCISE FOR CHAPTER 3: Systems of Linear Equations 1. Write your answers to the following using complete sentences. a. In a system of two linear equations in two variables, what do the equations in the system represent graphically? b. Suppose that when solving a system of linear equations, you obtain the equation 0= 5. i. Assuming your work is correct, what does this result tell you? ii. If you started with a system of two linear equations in two unknowns, what does this tell your about the graphs of the two equations?

5 Page 5 of 7 SUPPLEMENTAL EXERCISE FOR CHAPTER 3 - Systems of Linear Equations, Problem 1: c. Suppose that when solving a system of linear equations, you obtain the equation 3= 3. i. Assuming your work is correct, what does this result tell you? ii. If you started with a system of two linear equations in two unknowns, what does this tell you about the graphs of the two equations? d. What does it mean to say a system of two linear equations in two unknowns i. is dependent? ii. is independent? iii. is consistent? iv. is inconsistent? 2. Write and solve a system of linear equations for each problem below. Be sure to identify explicitly what each variable represents. a. A plane travels 300 miles against the wind in 5 hours then turns and travels 330 miles with the wind in 3 hours. Find the speed of the plane in still air and the speed of the wind.

6 Page 6 of 7 b. One solution is 20% alcohol and another is 50% alcohol. How many liters of each should be used to make 12 gallons of a solution that is 30% alcohol? c. The owner of The Daily Grind coffee shop wants to make a house blend by mixing three kinds of coffee: Colombian, Sumatran and Kenya Arabica. To test the new blend, she plans to make up a batch of 100 pounds of house blend and sell it for $9 per pound. She wants to use equal Price per Coffee pound Colombian $7.00 Sumatran $9.00 Kenya Arabica $ amounts of Sumatran and Colombian. The prices of the three types of coffee are given in the table. How much of each kind of coffee should she use to create her house blend?

7 Page 7 of 7 SUPPLEMENTAL EXERCISE FOR CHAPTER 4: Inequalities, Intervals and Graphs 1. When completed, each row of the table below should contain: an inequality statement, the interval(s) that correspond to the inequality statement, and the graph of the inequality. Complete the table by filling in the missing parts. Inequality Interval(s) Graph x 4 ( 2, ) 3 x < 5 (,1] ( 3, ) x 2 and x > 4 x 2 or x 2 2. Let A = { 2, 1, 0,1, 2}, B = { 0,1,2,3,4 }, and { 3, 2, 1} a. A B b. A B c. B C d. B C C =. Find