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 (
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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 a1 = 2, an = 3an-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) = 3x2 + 2x + 4. (3 points)13. Use the table below to find . (3 points)14. Given the matrices A and B below, find A + B and 3A. (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 Less
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