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MATH MECH 202 1.8.3 Practice_ Functions Santa Clara University

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Santa Clara University MATH MECH2021.8.3 Practice_ Functions Answer the following questions using what you've learned from this unit. Write your responses in the space provided. 1. ​Mark each of... the following graphs as (a) a function, but not one-to-one, (b) one-to-one function, or (c) not a function. In each case, explain how you know. (1 point each) Function not 1 to 1 It is an absolute function Fails horizontal line test Function not 1-1. It’s a greatest integer Function fails horizontal line test Function, not 1-1. Fails horizontal line test Not a function. Fails vertical line test Function one to one. Passes horizontal and vertical line test 2. ​Decide whether each of the following is linear or not linear. In each case, explain your answer. (1 point each) Linear. Only hits one x value for every y value on linear slope is inconsistent c. ​You have a secret that you tell to one person. Every hour, each of the people that know the secret tells one person. The number of people who know is ​N​, and ​t​ is the number of hours since you told the first person. Is ​N​ a linear function of ​t​? N=t^2+1, it’s a quadratic formula. It isn’t linear 3. ​Water freezes at 0 Celsius and 32 Fahrenheit. Water boils at 100 Celsius and 212 Fahrenheit. a. ​Write ​degrees Celsius​ as a linear function of ​degrees Fahrenheit (1 point)​. b. ​What is the slope of your linear equation? What does it mean? (1 point) c. ​What is the ​y​-intercept and what does it mean? (1 point) 4. ​Write the equation of the line represented by the following table (2 point): 5. ​Write the equation of the line represented by the following graph (2 points): y=2/3x-2 6. ​Match each equation with its possible graph shown below. In each case, explain the reasoning behind your choice. (1 point each) 7. ​Draw the graph of the area bounded by these inequalities (3 points): 8. ​Find the first five terms of the sequence given by ​a​1​ = 2, ​a​n​ = 3​a​n​-1​ - 1. (3 points) 9. ​The first term of an arithmetic sequence is 2 and the fourth term is 11. Find the sum of the first 50 terms. (3 points) The sum is 3675 10. ​For the following questions, use the system of equations (1 point each): a. ​Solve the system of equations using either the substitution method or the multiplication/addition method. ( b. ​Check your solution by writing the system as a matrix equation and using the inverse matrix. c. ​Verify your solution by graphing the system. Mark the point on your graph that represents the solution. 11. ​Find ​f​(2) and ​f​(​a​ + ​h​) when ​f​(​x​) = 3​x​2​ + 2​x​ + 4. (3 points) ​13. ​Use the table below to find . (3 points) ​​14. ​Given the matrices ​A​ and ​B​ below, find ​A​ + ​B​ and 3​A​. (3 points) 15. ​State the domain and range of each of the following functions (1 point each): a. b. c. 16. ​Decide whether each of the following is true or false, and circle the correct answer. (1 point each) a. ​A system of linear equations could have exactly two solutions. True / False False b. ​A system of linear equations could have an infinite number of solutions. True / False True c. ​If ​A​ and ​B​ are matrices, then ​AB​ is always equal to ​BA​. True / False True d. ​If ​f​ and ​g​ are functions, then is always equal to . True / False False [Show More]

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